Solved papers for NEET Physics Simple Harmonic Motion NEET PYQ-Simple Harmonic Motion

done NEET PYQ-Simple Harmonic Motion Total Questions - 44

• question_answer1) Two simple pendulums of length 0.5 m and 2.0 m respectively are given small linear displacement in one direction at die same time. They will again be in the same phase when the pendulum of shorter length has completed oscillations:                                                                                                                                           [AIPMT 1998]
  A)
         5                    
  done clear
  B)
        1                    
  done clear
  C)
   2        
  done clear
  D)
                    3
  done clear
  View Answer play_arrow

• question_answer2) A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system, if a mass 4 m is suspended from the same spring?                                       [AIPMT 1998]
  A)
   \[\frac{n}{4}\] 
  done clear
  B)
        4n                   
  done clear
  C)
   \[\frac{n}{2}\] 
  done clear
  D)
                    2 n
  done clear
  View Answer play_arrow

• question_answer3) A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force \[F\sin \omega t\]. If the amplitude of the particle is maximum for \[\omega ={{\omega }_{1}}\] and the energy of the particle maximum for\[\omega ={{\omega }_{2}},\] then :                                                          [AIPMT 1998]
  A)
   \[\omega ={{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{0}}\]
  done clear
  B)
                    \[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}={{\omega }_{0}}\]
  done clear
  C)
        \[{{\omega }_{1}}\ne {{\omega }_{0}}\] and\[{{\omega }_{2}}={{\omega }_{0}}\]       
  done clear
  D)
        \[{{\omega }_{1}}\ne {{\omega }_{0}}\] and  \[{{\omega }_{2}}\ne {{\omega }_{0}}\] where \[{{\omega }_{0}}\to \] natural angular frequency of oscillations of particle.
  done clear
  View Answer play_arrow

• question_answer4) The time period of a simple pendulum is 2s. If its length is increased by 4 times, then its period becomes: [AIPMT 1999]
  A)
   16 s                            
  done clear
  B)
   12 s                
  done clear
  C)
   8 s                              
  done clear
  D)
   4 s
  done clear
  View Answer play_arrow

• question_answer5) A pendulum is displaced to an angle \[\theta \] from its equilibrium position; then it will pass through its mean position with a velocity v equal to:                                                                                                          [AIPMT 2000]
  A)
         \[\sqrt{2gl}\]     
  done clear
  B)
        \[\sqrt{2gl\sin \theta }\]
  done clear
  C)
   \[\sqrt{2gl\cos \theta }\]             
  done clear
  D)
   \[\sqrt{2gl\,\,(1-\cos \theta )}\]
  done clear
  View Answer play_arrow

• question_answer6) Two simple harmonic motions given by \[x=A\sin (\omega t+\delta )\] and \[y=A\,\sin \left( \omega t+\delta +\frac{\pi }{2} \right)\] act on a particle simultaneously; then the motion of particle will be:                           [AIPMT 2000]
  A)
   circular anti-clockwise
  done clear
  B)
        circular clockwise
  done clear
  C)
        elliptical anti-clockwise
  done clear
  D)
   elliptical clockwise
  done clear
  View Answer play_arrow

• question_answer7) 

  A mass is suspended separately by two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] in successive order. The time periods of oscillations in the two cases are \[{{T}_{1}}\] and \[{{T}_{2}}\] respectively. If the same mass be suspended by connecting the two springs in parallel, (as shown in figure) then   the   time   period of oscillations is T. The correct relation is:  [AIPMT 2002]

  A)
         \[{{T}^{2}}=T_{1}^{2}+T_{2}^{2}\]                    
  done clear
  B)
   \[{{T}^{-2}}=T_{1}^{-2}+T_{2}^{-2}\]
  done clear
  C)
               \[{{T}^{-1}}=T_{1}^{-1}+T_{2}^{-1}\]
  done clear
  D)
        \[T={{T}_{1}}+{{T}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer8) When a damped harmonic oscillator completes 100 oscillations, its amplitude is reduced to \[\frac{1}{3}\] of its initial value. What will be its amplitude 'when it completes 200 oscillations?                                     [AIPMT 2002]
  A)
   \[\frac{1}{5}\] 
  done clear
  B)
                    \[\frac{2}{3}\]
  done clear
  C)
   \[\frac{1}{6}\] 
  done clear
  D)
                    \[\frac{1}{9}\]
  done clear
  View Answer play_arrow

• question_answer9) The displacement of particle between maximum potential energy position and maximum kinetic energy position in simple harmonic motion is :                                                                                           [AIPMT 2002]
  A)
   \[\pm \frac{a}{2}\]       
  done clear
  B)
                    \[\pm a\]
  done clear
  C)
   \[\pm \,2a\]      
  done clear
  D)
                    \[\pm \,1\]
  done clear
  View Answer play_arrow

• question_answer10) The potential energy of a simple harmonic oscillator when the particle is half way to its end point is:      [AIPMT 2003]
  A)
   \[\frac{1}{4}F\]
  done clear
  B)
                    \[\frac{1}{2}F\]
  done clear
  C)
   \[\frac{2}{3}F\]
  done clear
  D)
                    \[\frac{1}{8}F\] (where E is the total energy)
  done clear
  View Answer play_arrow

• question_answer11) The time period of a mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:                                            [AIPMT 2003]
  A)
   \[\frac{T}{2}\] 
  done clear
  B)
                    2T
  done clear
  C)
   \[\frac{T}{4}\] 
  done clear
  D)
                    T
  done clear
  View Answer play_arrow

• question_answer12) In case of a forced vibration, the resonance wave becomes very sharp when the:     [AIPMT 2003]
  A)
   applied periodic force is small
  done clear
  B)
        quality factor is small
  done clear
  C)
        damping force is small   
  done clear
  D)
   restoring force is small
  done clear
  View Answer play_arrow

• question_answer13) A particle of mass m oscillates with simple harmonic motion between points \[{{x}_{1}}\] and \[{{x}_{2}}\] the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph:              [AIPMT 2003]
  A)
          
  done clear
  B)
     
  done clear
  C)
        
  done clear
  D)
        
  done clear
  View Answer play_arrow

• question_answer14) Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?                                                                                                             [AIPMT (S) 2004]
  A)
   When v is maximum, a is maximum       
  done clear
  B)
        Value of a is zero, whatever may be the value of v
  done clear
  C)
        When v is zero, a is zero
  done clear
  D)
                    When v is maximum, a is zero
  done clear
  View Answer play_arrow

• question_answer15) Two springs of spring constants \[{{k}_{1}}\] and \[{{k}_{2}}\] are joined in series. The effective spring constant of the combination is given by:                                                                                                  [AIPMT (S) 2004]
  A)
   \[\sqrt{{{k}_{1}}{{k}_{2}}}\]  
  done clear
  B)
        \[({{k}_{1}}+{{k}_{2}})/2\]
  done clear
  C)
  \[{{k}_{1}}+{{k}_{2}}\]
  done clear
  D)
                    \[{{k}_{1}}{{k}_{2}}/({{k}_{1}}+{{k}_{2}})\]
  done clear
  View Answer play_arrow

• question_answer16) The circular motion of a particle with constant speed is:                       [AIPMT (S) 2005]
  A)
   simple harmonic but not periodic
  done clear
  B)
        periodic and simple harmonic
  done clear
  C)
   neither periodic nor simple harmonic        
  done clear
  D)
        periodic but not simple harmonic
  done clear
  View Answer play_arrow

• question_answer17) Particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is:                                                                                              [AIPMT (S) 2005]
  A)
         3 Hz   
  done clear
  B)
        2 Hz    
  done clear
  C)
   4 Hz
  done clear
  D)
                    1 Hz
  done clear
  View Answer play_arrow

• question_answer18) A rectangular block of mass m and area of cross-section A floats in a liquid of density                                                                                    \[\rho\] . If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Then:                                                                                                                                       [AIPMT (S) 2006]
  A)
                                                                         \[T\propto \,\,\sqrt{\rho }\]
  done clear
  B)
                                                                                     \[T\propto \,\,\frac{1}{\sqrt{A}}\]
  done clear
  C)
   \[T\propto \,\,\frac{1}{\rho }\]
  done clear
  D)
                    \[T\propto \,\,\frac{1}{\sqrt{m}}\]
  done clear
  View Answer play_arrow

• question_answer19) The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:                                                                                                                           [AIPMT (S) 2007]
  A)
  \[0.5\,\,\pi \]
  done clear
  B)
                    \[\pi \]
  done clear
  C)
   \[0.707\,\,\pi \]
  done clear
  D)
                    zero
  done clear
  View Answer play_arrow

• question_answer20) Two simple harmonic motions of angular frequency 100 and \[1000\text{ }rad~\,\,{{s}^{-1}}\] have the same displacement amplitude. The ratio of their maximum acceleration is                                                         [AIPMPT (S) 2008]
  A)
   \[1\,\,:10\]
  done clear
  B)
                    \[1\,\,:{{10}^{2}}\]
  done clear
  C)
   \[1\,\,:{{10}^{3}}\]    
  done clear
  D)
        \[1\,\,:{{10}^{4}}\]
  done clear
  View Answer play_arrow

• question_answer21) Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the phase difference between the oscillations of two points? [AIPMPT (S) 2008]
  A)
   \[\frac{\pi }{3}\]                       
  done clear
  B)
        \[\frac{2\pi }{3}\]
  done clear
  C)
   \[\pi \]              
  done clear
  D)
        \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer22) A point performs simple harmonic oscillation of period T and the equation of motion is given by\[x=c\sin (\omega t+\pi /6)\]. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity? [AIPMPT (S) 2008]
  A)
   \[\frac{T}{8}\]             
  done clear
  B)
        \[\frac{T}{6}\]
  done clear
  C)
   \[\frac{T}{3}\]             
  done clear
  D)
        \[\frac{T}{12}\]
  done clear
  View Answer play_arrow

• question_answer23) A simple pendulum performs simple harmonic motion about \[x=0\] with an amplitude \[a\] and time period T. The speed of the pendulum at \[x=\frac{a}{2}\] will be                                                                   [AIPMT (S) 2009]
  A)
   \[\frac{\pi a\sqrt{3}}{2T}\]        
  done clear
  B)
        \[\frac{\pi a}{T}\]                     
  done clear
  C)
   \[\frac{3{{\pi }^{2}}a}{T}\]   
  done clear
  D)
        \[\frac{\pi a\sqrt{3}}{T}\]
  done clear
  View Answer play_arrow

• question_answer24) Which one of the following equations of motion represents simple harmonic motion?                [AIPMT (S) 2009]
  A)
   Acceleration \[=-{{k}_{0}}x+{{k}_{1}}{{x}^{2}}\]
  done clear
  B)
   Acceleration \[=-\,k\,(x+a)\]
  done clear
  C)
   Acceleration \[=\,k\,(x+a)\]
  done clear
  D)
   Acceleration \[=kx\] where \[k,\,{{k}_{0}},\,{{k}_{1}}\] and a are all positive.
  done clear
  View Answer play_arrow

• question_answer25) The displacement of a particle along the x axis is given by \[x=a{{\sin }^{2}}\omega t\]. The motion of the particle corresponds to                                                                                                                         [AIPMT (S) 2010]
  A)
   simple harmonic motion of frequency \[\omega /\pi \]
  done clear
  B)
   simple harmonic motion of frequency \[3\omega /2\pi \]
  done clear
  C)
   non simple harmonic motion
  done clear
  D)
   simple harmonic motion of frequency \[\omega /2\pi \]
  done clear
  View Answer play_arrow

• question_answer26) The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be                                                                   [AIPMT (S) 2010]
  A)
   T                    
  done clear
  B)
        \[T/\sqrt{2}\]
  done clear
  C)
   \[2\,T\]            
  done clear
  D)
        \[\sqrt{2}T\]
  done clear
  View Answer play_arrow

• question_answer27) Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beat/s when both the wires oscillate together would be                                                                                                                                    [AIPMT (M) 2011]
  A)
   0.02    
  done clear
  B)
        0.03    
  done clear
  C)
   0.04   
  done clear
  D)
        0.01
  done clear
  View Answer play_arrow

• question_answer28) Two particle are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is                                                                                           [AIPMT (M) 2011]
  A)
   zero                 
  done clear
  B)
        \[\frac{2\pi }{3}\]
  done clear
  C)
   \[\pi \]              
  done clear
  D)
        \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer29) Two waves are represented by the equations \[{{y}_{1}}-a\sin (\omega t+kx+0.57)m\] and \[{{y}_{2}}-a\cos \,(\omega t+kx)m,\] in, where x is in metre and t in second. The phase difference between them is                                                                                                                                 [AIPMT (S) 2011]
  A)
   1.25 rad        
  done clear
  B)
        1.57 rad          
  done clear
  C)
   0.57 rad        
  done clear
  D)
        1.0 rad
  done clear
  View Answer play_arrow

• question_answer30) 

  Out of the following functions representing motion of a particle which represents SHM  [AIPMT (S) 2011]

  I. \[y=\sin \omega t-\cos \omega t\]           II. \[y={{\sin }^{3}}\omega t\]

  III. \[y=5\cos \left( \frac{3\pi }{4}-3\,\omega t \right)\]        IV. \[y=1+\omega t+{{\omega }^{2}}{{t}^{2}}\]

  A)
   Only (IV) does not represent SHM          
  done clear
  B)
   (I) and (III)
  done clear
  C)
   (I) and (II)
  done clear
  D)
   Only (I)
  done clear
  View Answer play_arrow

• question_answer31) A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?    [AIPMT (S) 2011]
  A)
                                     
  done clear
  B)
   
  done clear
  C)
   
  done clear
  D)
   
  done clear
  View Answer play_arrow

• question_answer32) 

  The oscillation of a body on a smooth horizontal surface is represented by the equation,\[X=A\cos (\omega t)\]                                                                                                                                                                       [NEET 2014]

  where    \[X=\] displacement at time t

  \[\omega =\] frequency of oscillation

  Which one of the following graphs shows correctly the variation a with t?

  A)
   
  done clear
  B)
   
  done clear
  C)
  
  done clear
  D)
              Here,   \[a=\] acceleration at time t \[T=\] time period
  done clear
  View Answer play_arrow

• question_answer33) When two displacements represented by \[{{y}_{1}}=a\sin (\omega t)\] and \[{{y}_{2}}=b\cos \,(\omega t)\] are superimposed, the motion is                                                                                              [NEET  2015]
  A)
   not a simple harmonic
  done clear
  B)
   simple harmonic with amplitude \[\frac{a}{b}\]
  done clear
  C)
   simple harmonic with amplitude \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
  done clear
  D)
   simple harmonic with amplitude \[\frac{(a+b)}{2}\]
  done clear
  View Answer play_arrow

• question_answer34) A particle is executing SHM along a straight line. Its velocities at distances \[{{x}_{1}}\] and \[{{x}_{2}}\] from the mean position are \[{{v}_{1}}\] and \[{{v}_{2}},\] respectively. Its time period is                         [NEET  2015]
  A)
   \[2\pi \sqrt{\frac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}\]           
  done clear
  B)
        \[2\pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}\]
  done clear
  C)
   \[2\pi \sqrt{\frac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\]           
  done clear
  D)
        \[2\pi \sqrt{\frac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer35) A particle is executing a simple harmonic motion. Its maximum acceleration is \[\alpha \] and maximum velocity is \[\beta \]. Then, its time period of vibration will be                                                                             [NEET (Re) 2015]
  A)
   \[\frac{{{\beta }^{2}}}{{{\alpha }^{2}}}\]                
  done clear
  B)
       \[\frac{\alpha }{\beta }\]
  done clear
  C)
   \[\frac{{{\beta }^{2}}}{\alpha }\]                    
  done clear
  D)
        \[\frac{2\pi \beta }{\alpha }\]
  done clear
  View Answer play_arrow

• question_answer36) A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is \[{{U}_{1}},\] at wavelength 500 nm is \[{{U}_{2}}\] and that at 1000 nm is \[{{U}_{3}}\]. Wien's constant, \[b=2.88\times {{10}^{6}}\text{ }nmK\]. Which of the following is correct?                                                           [NEET - 2016]
  A)
   \[{{U}_{1}}=0\]         
  done clear
  B)
        \[{{U}_{3}}=0\]
  done clear
  C)
   \[{{U}_{1}}>\text{ }{{U}_{2}}\]        
  done clear
  D)
        \[{{U}_{2}}>\text{ }{{U}_{1}}\]
  done clear
  View Answer play_arrow

• question_answer37) A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is  [NEET-2017]
  A)
   \[\frac{2\pi }{\sqrt{3}}\]           
  done clear
  B)
        \[\frac{\sqrt{5}}{\pi }\]
  done clear
  C)
   \[\frac{\sqrt{5}}{2\pi }\]           
  done clear
  D)
        \[\frac{4\pi }{\sqrt{5}}\]
  done clear
  View Answer play_arrow

• question_answer38) 

  Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are \[{{K}_{1}}\] and \[{{K}_{2}}\]. The thermal conductivity of the composite rod will be                                                                     [NEET-2017]

  A)
   \[2({{K}_{1}}+{{K}_{2}})\]    
  done clear
  B)
        \[\frac{{{K}_{1}}+{{K}_{2}}}{2}\]
  done clear
  C)
  \[\frac{3({{K}_{1}}+{{K}_{2}})}{2}\]  
  done clear
  D)
        \[{{K}_{1}}+{{K}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer39) A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
  A)
   1800   
  done clear
  B)
        225
  done clear
  C)
   450                 
  done clear
  D)
        1000
  done clear
  View Answer play_arrow

• question_answer40) A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is \[20\text{ }m/{{s}^{2}}\]at a distance of 5 m from the mean position. The time period of oscillation is                                                                                           [NEET - 2018]
  A)
   \[\text{2s}\]       
  done clear
  B)
   \[\pi \text{s}\]   
  done clear
  C)
   \[2\pi \text{s}\] 
  done clear
  D)
   \[1\text{s}\]
  done clear
  View Answer play_arrow

• question_answer41) Average velocity of a particle executing SHM in one complete vibration is:            [NEET 2019]
  A)
   \[\frac{A{{\omega }^{2}}}{2}\]          
  done clear
  B)
        Zero
  done clear
  C)
   \[\frac{A\omega }{2}\]              
  done clear
  D)
        \[A\omega \]
  done clear
  View Answer play_arrow

• question_answer42) The displacement of a particle executing simple harmonic motion is given by\[y={{A}_{0}}+A\,sin\omega t+B\,cos\omega t\]. Then the amplitude of its oscillation is given by:                                                                  [NEET 2019]
  A)
   \[\sqrt{A_{0}^{2}+{{(A+B)}^{2}}}\]
  done clear
  B)
   A+B
  done clear
  C)
   \[{{A}_{0}}=\sqrt{{{A}^{2}}+{{B}^{2}}}\]
  done clear
  D)
   \[\sqrt{{{A}^{2}}+{{B}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer43) 

  The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.

  [NEET 2019]

  Y-projection of the radius vector of rotating particle P is:

  A)
  \[(y)t=3cos\left( \frac{3\pi t}{2} \right)\], where y in m
  done clear
  B)
   \[(y)t=3cos\left( \frac{\pi t}{2} \right)\], where y in m
  done clear
  C)
   \[(y)t=-3cos2\pi t\], where y in m
  done clear
  D)
   \[(y)t=4\sin \left( \frac{\pi t}{2} \right)\], where y in m
  done clear
  View Answer play_arrow

• question_answer44) The phase difference between displacement and acceleration of a particle in a simple harmonic motion is: [NEET 2020]
  A)
   \[\frac{3\pi }{2}\text{rad}\]       
  done clear
  B)
        \[\frac{\pi }{2}\text{rad}\]
  done clear
  C)
   zero                 
  done clear
  D)
        \[\pi \text{ rad}\]          
  done clear
  View Answer play_arrow