# 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

B)
1

C)
2

D)
3

• 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)
$\frac{n}{4}$

B)
4n

C)
$\frac{n}{2}$

D)
2 n

• 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 ${{\omega }_{2}}\ne {{\omega }_{0}}$

B)
${{\omega }_{1}}={{\omega }_{0}}$ and ${{\omega }_{2}}={{\omega }_{0}}$

C)
${{\omega }_{1}}\ne {{\omega }_{0}}$ and${{\omega }_{2}}={{\omega }_{0}}$

D)
${{\omega }_{1}}\ne {{\omega }_{0}}$ and  ${{\omega }_{2}}\ne {{\omega }_{0}}$ where ${{\omega }_{0}}\to$ natural angular frequency of oscillations of particle.

• 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

B)
12 s

C)
8 s

D)
4 s

• 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)
$\sqrt{2gl}$

B)
$\sqrt{2gl\sin \theta }$

C)
$\sqrt{2gl\cos \theta }$

D)
$\sqrt{2gl\,\,(1-\cos \theta )}$

• 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

B)
circular clockwise

C)
elliptical anti-clockwise

D)
elliptical clockwise

• 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)
${{T}^{2}}=T_{1}^{2}+T_{2}^{2}$

B)
${{T}^{-2}}=T_{1}^{-2}+T_{2}^{-2}$

C)
${{T}^{-1}}=T_{1}^{-1}+T_{2}^{-1}$

D)
$T={{T}_{1}}+{{T}_{2}}$

• 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)
$\frac{1}{5}$

B)
$\frac{2}{3}$

C)
$\frac{1}{6}$

D)
$\frac{1}{9}$

• question_answer9) The displacement of particle between maximum potential energy position and maximum kinetic energy position in simple harmonic motion is :                                                                                           [AIPMT 2002]

A)
$\pm \frac{a}{2}$

B)
$\pm a$

C)
$\pm \,2a$

D)
$\pm \,1$

• question_answer10) The potential energy of a simple harmonic oscillator when the particle is half way to its end point is:      [AIPMT 2003]

A)
$\frac{1}{4}F$

B)
$\frac{1}{2}F$

C)
$\frac{2}{3}F$

D)
$\frac{1}{8}F$ (where E is the total energy)

• 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)
$\frac{T}{2}$

B)
2T

C)
$\frac{T}{4}$

D)
T

• question_answer12) In case of a forced vibration, the resonance wave becomes very sharp when the:     [AIPMT 2003]

A)
applied periodic force is small

B)
quality factor is small

C)
damping force is small

D)
restoring force is small

• 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)

B)

C)

D)

• 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

B)
Value of a is zero, whatever may be the value of v

C)
When v is zero, a is zero

D)
When v is maximum, a is zero

• 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)
$\sqrt{{{k}_{1}}{{k}_{2}}}$

B)
$({{k}_{1}}+{{k}_{2}})/2$

C)
${{k}_{1}}+{{k}_{2}}$

D)
${{k}_{1}}{{k}_{2}}/({{k}_{1}}+{{k}_{2}})$

• question_answer16) The circular motion of a particle with constant speed is:                       [AIPMT (S) 2005]

A)
simple harmonic but not periodic

B)
periodic and simple harmonic

C)
neither periodic nor simple harmonic

D)
periodic but not simple harmonic

• 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

B)
2 Hz

C)
4 Hz

D)
1 Hz

• 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)
$T\propto \,\,\sqrt{\rho }$

B)
$T\propto \,\,\frac{1}{\sqrt{A}}$

C)
$T\propto \,\,\frac{1}{\rho }$

D)
$T\propto \,\,\frac{1}{\sqrt{m}}$

• question_answer19) The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:                                                                                                                           [AIPMT (S) 2007]

A)
$0.5\,\,\pi$

B)
$\pi$

C)
$0.707\,\,\pi$

D)
zero

• 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)
$1\,\,:10$

B)
$1\,\,:{{10}^{2}}$

C)
$1\,\,:{{10}^{3}}$

D)
$1\,\,:{{10}^{4}}$

• 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)
$\frac{\pi }{3}$

B)
$\frac{2\pi }{3}$

C)
$\pi$

D)
$\frac{\pi }{6}$

• 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)
$\frac{T}{8}$

B)
$\frac{T}{6}$

C)
$\frac{T}{3}$

D)
$\frac{T}{12}$

• 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)
$\frac{\pi a\sqrt{3}}{2T}$

B)
$\frac{\pi a}{T}$

C)
$\frac{3{{\pi }^{2}}a}{T}$

D)
$\frac{\pi a\sqrt{3}}{T}$

• question_answer24) Which one of the following equations of motion represents simple harmonic motion?                [AIPMT (S) 2009]

A)
Acceleration $=-{{k}_{0}}x+{{k}_{1}}{{x}^{2}}$

B)
Acceleration $=-\,k\,(x+a)$

C)
Acceleration $=\,k\,(x+a)$

D)
Acceleration $=kx$ where $k,\,{{k}_{0}},\,{{k}_{1}}$ and a are all positive.

• 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 $\omega /\pi$

B)
simple harmonic motion of frequency $3\omega /2\pi$

C)
non simple harmonic motion

D)
simple harmonic motion of frequency $\omega /2\pi$

• 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

B)
$T/\sqrt{2}$

C)
$2\,T$

D)
$\sqrt{2}T$

• 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

B)
0.03

C)
0.04

D)
0.01

• 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

B)
$\frac{2\pi }{3}$

C)
$\pi$

D)
$\frac{\pi }{6}$

• 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)

B)

C)

D)

• 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

B)
(I) and (III)

C)
(I) and (II)

D)
Only (I)

• 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)

B)

C)

D)

• 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)

B)

C)

D)
Here,   $a=$ acceleration at time t $T=$ time period

• 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

B)
simple harmonic with amplitude $\frac{a}{b}$

C)
simple harmonic with amplitude $\sqrt{{{a}^{2}}+{{b}^{2}}}$

D)
simple harmonic with amplitude $\frac{(a+b)}{2}$

• 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)
$2\pi \sqrt{\frac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}$

B)
$2\pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}$

C)
$2\pi \sqrt{\frac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}$

D)
$2\pi \sqrt{\frac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}$

• 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)
$\frac{{{\beta }^{2}}}{{{\alpha }^{2}}}$

B)
$\frac{\alpha }{\beta }$

C)
$\frac{{{\beta }^{2}}}{\alpha }$

D)
$\frac{2\pi \beta }{\alpha }$

• 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)
${{U}_{1}}=0$

B)
${{U}_{3}}=0$

C)
${{U}_{1}}>\text{ }{{U}_{2}}$

D)
${{U}_{2}}>\text{ }{{U}_{1}}$

• 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)
$\frac{2\pi }{\sqrt{3}}$

B)
$\frac{\sqrt{5}}{\pi }$

C)
$\frac{\sqrt{5}}{2\pi }$

D)
$\frac{4\pi }{\sqrt{5}}$

• 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)
$2({{K}_{1}}+{{K}_{2}})$

B)
$\frac{{{K}_{1}}+{{K}_{2}}}{2}$

C)
$\frac{3({{K}_{1}}+{{K}_{2}})}{2}$

D)
${{K}_{1}}+{{K}_{2}}$

• 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

B)
225

C)
450

D)
1000

• 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)
$\text{2s}$

B)
$\pi \text{s}$

C)
$2\pi \text{s}$

D)
$1\text{s}$

• question_answer41) Average velocity of a particle executing SHM in one complete vibration is:            [NEET 2019]

A)
$\frac{A{{\omega }^{2}}}{2}$

B)
Zero

C)
$\frac{A\omega }{2}$

D)
$A\omega$

• 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)
$\sqrt{A_{0}^{2}+{{(A+B)}^{2}}}$

B)
A+B

C)
${{A}_{0}}=\sqrt{{{A}^{2}}+{{B}^{2}}}$

D)
$\sqrt{{{A}^{2}}+{{B}^{2}}}$

• 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

B)
$(y)t=3cos\left( \frac{\pi t}{2} \right)$, where y in m

C)
$(y)t=-3cos2\pi t$, where y in m

D)
$(y)t=4\sin \left( \frac{\pi t}{2} \right)$, where y in m

• question_answer44) The phase difference between displacement and acceleration of a particle in a simple harmonic motion is: [NEET 2020]

A)
$\frac{3\pi }{2}\text{rad}$

B)
$\frac{\pi }{2}\text{rad}$

C)
zero

D)
$\pi \text{ rad}$