JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Displacement of S.H.M. and Phase Total Questions - 26

• question_answer1)
  The phase of a particle executing simple harmonic motion is \[\frac{\pi }{2}\] when it has                                             [MP PET 1985]
  A)
             Maximum velocity              done clear
  B)
             Maximum acceleration done clear
  C)
             Maximum energy               done clear
  D)
             Maximum displacement done clear
  View Solution play_arrow

• question_answer2)
  A particle starts S.H.M. from the mean position. Its amplitude is A and time period is T. At the time when its speed is half of the maximum speed, its displacement y is [Haryana CEE 1996; CBSE PMT 1996; MH CET 2002]
  A)
             \[\frac{A}{2}\]                      done clear
  B)
             \[\frac{A}{\sqrt{2}}\] done clear
  C)
             \[\frac{A\sqrt{3}}{2}\]      done clear
  D)
             \[\frac{2A}{\sqrt{3}}\] done clear
  View Solution play_arrow

• question_answer3)
  The amplitude and the periodic time of a S.H.M. are 5cm and 6sec respectively. At a distance of 2.5cm away from the mean position, the phase will be
  A)
             \[5\pi /12\]                            done clear
  B)
             \[\pi /4\] done clear
  C)
             \[\pi /3\]                                 done clear
  D)
             \[\pi /6\] done clear
  View Solution play_arrow

• question_answer4)
  Two equations of two S.H.M. are \[y=a\sin \,(\omega \,t-\alpha )\] and\[y=b\cos (\omega \,t-\alpha )\]. The phase difference between the two is                                                               [MP PMT 1985]
  A)
             0°    done clear
  B)
             a° done clear
  C)
             90° done clear
  D)
             180° done clear
  View Solution play_arrow

• question_answer5)
  The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is \[\pi /2\] radian, then the equation of S.H.M. will be
  A)
             \[y=0.5\sin 5\pi t\]             done clear
  B)
             \[y=0.5\sin 4\pi t\] done clear
  C)
             \[y=0.5\sin 2.5\pi t\]          done clear
  D)
             \[y=0.5\cos 5\pi t\] done clear
  View Solution play_arrow

• question_answer6)
  The equation of S.H.M. is \[y=a\sin (2\pi nt+\alpha )\], then its phase at time t is                                              [DPMT 2001]
  A)
             \[2\pi nt\]                              done clear
  B)
             \[\alpha \] done clear
  C)
             \[2\pi nt+\alpha \]              done clear
  D)
             \[2\pi t\] done clear
  View Solution play_arrow

• question_answer7)
  A particle is oscillating according to the equation\[X=7\cos 0.5\pi t\], where t is in second. The point moves from the position of equilibrium to maximum displacement in time                                            [CPMT 1989]
  A)
             4.0 sec                                      done clear
  B)
             2.0 sec done clear
  C)
             1.0 sec                                      done clear
  D)
             0.5 sec done clear
  View Solution play_arrow

• question_answer8)
  A simple harmonic oscillator has an  amplitude a and time period T. The time required by it to travel from x = a to x = a / 2 is      [CBSE PMT 1992; SCRA 1996; BHU 1997]
  A)
             T / 6                                          done clear
  B)
             T / 4 done clear
  C)
             T / 3                                          done clear
  D)
             T / 2 done clear
  View Solution play_arrow

• question_answer9)
  Which of the following expressions represent simple harmonic motion                                  [Roorkee 1999]
  A)
             \[x=A\sin (\omega \,t+\delta )\]                                     done clear
  B)
             \[x=B\cos (\omega \,t+\varphi )\] done clear
  C)
             \[x=A\tan (\omega \,t+\varphi )\]                                  done clear
  D)
             \[x=A\sin \omega \,t\cos \omega \,t\] done clear
  View Solution play_arrow

• question_answer10)
  A \[1.00\times {{10}^{-20}}kg\] particle is vibrating with simple harmonic motion with a period of \[1.00\times {{10}^{-5}}sec\] and a maximum speed of \[1.00\times {{10}^{3}}m/s\]. The maximum displacement of the particle is                                                                  [AMU (Med.) 1999]
  A)
             1.59 mm                                  done clear
  B)
             1.00 m done clear
  C)
             10 m                                         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer11)
  The phase (at a time t) of a particle in simple harmonic motion tells                                          [AMU (Engg.) 1999]
  A)
             Only the position of the particle at time t done clear
  B)
             Only the direction of motion of the particle at time t done clear
  C)
             Both the position and direction of motion of the particle at time t done clear
  D)
             Neither the position of the particle nor its direction of motion at time t done clear
  View Solution play_arrow

• question_answer12)
  A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true                                              [AMU (Engg.) 1999]
  A)
             The particle so moving executes S.H.M. done clear
  B)
             The projection of the particle on any one of the diameters executes S.H.M. done clear
  C)
             The projection of the particle on any of the diameters executes S.H.M. done clear
  D)
             None of the above done clear
  View Solution play_arrow

• question_answer13)
  A particle is executing simple harmonic motion with a period of T seconds and amplitude a metre. The shortest time it takes to reach a point \[\frac{a}{\sqrt{2}}m\] from its mean position in seconds is             [EAMCET (Med.) 2000]
  A)
             T     done clear
  B)
             T/4 done clear
  C)
             T/8 done clear
  D)
             T/16 done clear
  View Solution play_arrow

• question_answer14)
  A simple harmonic motion is represented by \[F(t)=10\sin \,(20\,t+0.5)\]. The amplitude of the S.H.M. is [DPMT 1998; CBSE PMT 2000; MH CET 2001]
  A)
             a = 30                                       done clear
  B)
             a = 20 done clear
  C)
             a = 10                                       done clear
  D)
             a = 5 done clear
  View Solution play_arrow

• question_answer15)
  Which of the following equation does not represent a simple harmonic motion                 [Kerala (Med.) 2002]
  A)
             \[y=a\sin \omega \,t\]      done clear
  B)
             \[y=a\cos \omega \,t\] done clear
  C)
             \[y=a\sin \omega \,t+b\cos \omega \,t\]                    done clear
  D)
             \[y=a\tan \omega \,t\] done clear
  View Solution play_arrow

• question_answer16)
  A particle in S.H.M. is described by the displacement function \[x(t)=a\cos (\omega t+\theta )\]. If the initial \[(t=0)\] position of the particle is 1 cm and its initial velocity is \[\pi \,cm/s\]. The angular frequency of the particle is \[\pi \,rad/s\], then it?s amplitude is                                                                  [AMU (Med.) 2002]
  A)
             1 cm                                          done clear
  B)
             \[\sqrt{2}\,cm\] done clear
  C)
             2 cm                                          done clear
  D)
             2.5 cm done clear
  View Solution play_arrow

• question_answer17)
  A particle executes a simple harmonic motion of time period T. Find the time taken by the particle to go directly from its mean position to half the amplitude            [UPSEAT 2002]
  A)
             T / 2                                          done clear
  B)
             T / 4 done clear
  C)
             T / 8                                          done clear
  D)
             T / 12 done clear
  View Solution play_arrow

• question_answer18)
  A particle executing simple harmonic motion along y-axis has its motion described by the equation \[y=A\sin (\omega \,t)+B\]. The amplitude of the simple harmonic motion is [Orissa JEE 2003]
  A)
             A     done clear
  B)
             B done clear
  C)
             A + B                                         done clear
  D)
             \[\sqrt{A+B}\] done clear
  View Solution play_arrow

• question_answer19)
  A particle executing S.H.M. of amplitude 4 cm and T = 4 sec. The time taken by it to move from positive extreme position to half the amplitude is                                [BHU 1995]
  A)
             1 sec                                         done clear
  B)
             1/3 sec done clear
  C)
             2/3 sec                                     done clear
  D)
             \[\sqrt{3/2}\]sec done clear
  View Solution play_arrow

• question_answer20)
  Which one of the following is a simple harmonic motion [CBSE PMT 1994]
  A)
             Wave moving through a string fixed at both ends done clear
  B)
             Earth spinning about its own axis done clear
  C)
             Ball bouncing between two rigid vertical walls done clear
  D)
             Particle moving in a circle with uniform speed done clear
  View Solution play_arrow

• question_answer21)
  A particle is moving in a circle with uniform speed. Its motion is  [CPMT 1978; CBSE PMT 2005]
  A)
             Periodic and simple harmonic                                           done clear
  B)
             Periodic but not simple harmonic done clear
  C)
             A periodic done clear
  D)
             None of the above done clear
  View Solution play_arrow

• question_answer22)
  Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)\]and \[{{y}_{2}}=0.1\cos \pi t.\] The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is                                                                  [AIEEE 2005]
  A)
             \[\frac{-\pi }{3}\]                 done clear
  B)
             \[\frac{\pi }{6}\] done clear
  C)
             \[\frac{-\pi }{6}\]                 done clear
  D)
             \[\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer23)
  Two particles are executing S.H.M. The equation of their motion are \[{{y}_{1}}=10\sin \left( \omega \,t+\frac{\pi T}{4} \right),\]\[{{y}_{2}}=25\sin \,\left( \omega \,t+\frac{\sqrt{3}\pi T}{4} \right)\]. What is the ratio of their amplitude                    [DCE 1996]
  A)
             1 : 1                                           done clear
  B)
             2 : 5 done clear
  C)
             1 : 2                                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer24)
  The periodic time of a body executing simple harmonic motion is 3 sec. After how much interval from time t = 0, its displacement will be half of its amplitude             [BHU 1998]
  A)
             \[\frac{1}{8}\]sec                done clear
  B)
             \[\frac{1}{6}\]sec done clear
  C)
             \[\frac{1}{4}\]sec                done clear
  D)
             \[\frac{1}{3}\]sec done clear
  View Solution play_arrow

• question_answer25)
  A system exhibiting S.H.M. must possess            [KCET 1994]
  A)
             Inertia only                            done clear
  B)
             Elasticity as well as inertia done clear
  C)
             Elasticity, inertia and an external force done clear
  D)
             Elasticity only done clear
  View Solution play_arrow

• question_answer26)
   If \[x=a\sin \left( \omega t+\frac{\pi }{6} \right)\] and \[{x}'=a\cos \omega t\], then what is the phase difference between the two waves             [RPET 1996]
  A)
             p / 3                                          done clear
  B)
             p / 6 done clear
  C)
             p / 2                                          done clear
  D)
             p done clear
  View Solution play_arrow