JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Energy of Simple Harmonic Motion Total Questions - 34

• question_answer1)
  The total energy of a particle executing S.H.M. is proportional to [CPMT 1974, 78; EAMCET 1994; RPET 1999; MP PMT 2001; Pb. PMT 2002; MH CET 2002]
  A)
             Displacement from equilibrium position done clear
  B)
             Frequency of oscillation done clear
  C)
             Velocity in equilibrium position done clear
  D)
             Square of amplitude of motion done clear
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• question_answer2)
   A particle executes simple harmonic motion along a straight line with an amplitude A. The potential energy is maximum when the displacement is                                         [CPMT 1982]
  A)
             \[\pm A\]                               done clear
  B)
             Zero done clear
  C)
             \[\pm \frac{A}{2}\]            done clear
  D)
             \[\pm \frac{A}{\sqrt{2}}\] done clear
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• question_answer3)
  A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and half kinetic [NCERT 1984; MNR 1995;  RPMT 1995; DCE 2000; UPSEAT 2000]
  A)
             1 cm                                          done clear
  B)
             \[\sqrt{2}\]cm done clear
  C)
             3 cm                                          done clear
  D)
             \[2\sqrt{2}\]cm done clear
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• question_answer4)
  For a particle executing simple harmonic motion, the kinetic energy K is given by \[K={{K}_{o}}{{\cos }^{2}}\omega t\]. The maximum value of potential energy is                                                           [CPMT 1981]
  A)
             \[{{K}_{0}}\]                          done clear
  B)
             Zero done clear
  C)
             \[\frac{{{K}_{0}}}{2}\]       done clear
  D)
             Not obtainable done clear
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• question_answer5)
  The potential energy of a particle with displacement X is U(X). The motion is simple harmonic, when (K is a positive constant)                                                                          [CPMT 1982]
  A)
             \[U=-\frac{K{{X}^{2}}}{2}\]     done clear
  B)
             \[U=K{{X}^{2}}\] done clear
  C)
             \[U=K\]                                   done clear
  D)
             \[U=KX\] done clear
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• question_answer6)
  The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement  (amplitude = a) is [MP PMT 1987; CPMT 1990; DPMT 1996;  MH CET 1997, 99; AFMC 1999; CPMT 2000]
  A)
             \[\frac{a}{2}\]                       done clear
  B)
             \[a\sqrt{2}\] done clear
  C)
             \[\frac{a}{\sqrt{2}}\]         done clear
  D)
             \[\frac{a\sqrt{2}}{3}\] done clear
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• question_answer7)
   The total energy of the body executing S.H.M. is E. Then the kinetic energy when the displacement is half of the amplitude, is [RPMT 1994, 96; CBSE PMT 1995; JIPMER 2002]
  A)
             \[\frac{E}{2}\]                       done clear
  B)
             \[\frac{E}{4}\] done clear
  C)
             \[\frac{3E}{4}\]                    done clear
  D)
             \[\frac{\sqrt{3}}{4}E\] done clear
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• question_answer8)
  The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be                                                          [DPMT 2001]
  A)
             18 J done clear
  B)
             10 J done clear
  C)
             12 J done clear
  D)
             2.5 J done clear
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• question_answer9)
  The angular velocity and the amplitude of a simple pendulum is \[\omega \] and a respectively. At a displacement X from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is          [CBSE PMT 1991]
  A)
             \[{{X}^{2}}{{\omega }^{2}}/({{a}^{2}}-{{X}^{2}}{{\omega }^{2}})\]  done clear
  B)
             \[{{X}^{2}}/({{a}^{2}}-{{X}^{2}})\] done clear
  C)
             \[({{a}^{2}}-{{X}^{2}}{{\omega }^{2}})/{{X}^{2}}{{\omega }^{2}}\]  done clear
  D)
             \[({{a}^{2}}-{{X}^{2}})/{{X}^{2}}\] done clear
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• question_answer10)
  When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is [CBSE PMT 1993; EAMCET (Engg.) 1995;                      MP PMT 1994, 2000; MP PET 1995, 96, 2002]
  A)
             \[a/4\]                                     done clear
  B)
             \[a/3\] done clear
  C)
             \[a/2\]                                     done clear
  D)
             \[2a/3\] done clear
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• question_answer11)
  A particle of mass 10 gm is describing S.H.M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is                                [MP PMT 1996]
  A)
             \[37.5{{\pi }^{2}}ergs\]     done clear
  B)
             \[3.75{{\pi }^{2}}ergs\] done clear
  C)
             \[375{{\pi }^{2}}ergs\]      done clear
  D)
             \[0.375{{\pi }^{2}}ergs\] done clear
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• question_answer12)
  When the displacement is half the amplitude, the ratio of potential energy to the total energy is [CPMT 1999; JIPMER 2000; Kerala PET 2002]
  A)
             \[\frac{1}{2}\]                       done clear
  B)
             \[\frac{1}{4}\] done clear
  C)
             \[1\]                                         done clear
  D)
             \[\frac{1}{8}\] done clear
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• question_answer13)
  The P.E. of a particle executing SHM at a distance x from its equilibrium position is [Roorkee 1992; CPMT 1997; RPMT 1999]
  A)
             \[\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}\]                     done clear
  B)
             \[\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\] done clear
  C)
             \[\frac{1}{2}m{{\omega }^{2}}({{a}^{2}}-{{x}^{2}})\]             done clear
  D)
             Zero                                          done clear
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• question_answer14)
  A vertical mass-spring system executes simple harmonic oscillations with a period of 2 s. A quantity of this system which exhibits simple harmonic variation with a period of 1 s is                                                   [SCRA 1998]
  A)
             Velocity done clear
  B)
             Potential energy done clear
  C)
             Phase difference between acceleration and displacement done clear
  D)
             Difference between kinetic energy and potential energy done clear
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• question_answer15)
  For any S.H.M., amplitude is 6 cm. If instantaneous potential energy is half the total energy then distance of particle from its mean position is                    [RPET 2000]
  A)
             3 cm                                          done clear
  B)
             4.2 cm done clear
  C)
             5.8 cm                                      done clear
  D)
             6 cm done clear
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• question_answer16)
  A body of mass \[1\,kg\] is executing simple harmonic motion. Its displacement \[y(cm)\] at t seconds is given by \[y=6\sin (100t+\pi /4)\]. Its maximum kinetic energy is  [EAMCET (Engg.) 2000]
  A)
             6 J   done clear
  B)
             18 J done clear
  C)
             24 J done clear
  D)
             36 J done clear
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• question_answer17)
  A particle is executing simple harmonic motion with frequency f. The frequency at which its kinetic energy change into potential energy is                                [MP PET 2000]
  A)
             f/2  done clear
  B)
             f done clear
  C)
             2 f   done clear
  D)
             4 f done clear
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• question_answer18)
  There is a body having mass m and performing S.H.M. with amplitude a. There is a restoring force \[F=-Kx\], where x is the displacement. The total energy of body depends upon  [CBSE PMT 2001]
  A)
             K, x                                            done clear
  B)
             K, a done clear
  C)
             K, a, x                                       done clear
  D)
             K, a, v done clear
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• question_answer19)
  The total energy of a particle executing S.H.M. is 80 J. What is the potential energy when the particle is at a distance of 3/4 of amplitude from the mean position  [Kerala (Engg.) 2001]
  A)
             60 J                                            done clear
  B)
             10 J done clear
  C)
             40 J done clear
  D)
             45 J done clear
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• question_answer20)
  In a simple harmonic oscillator, at the mean position  [AIEEE 2002]
  A)
             Kinetic energy is minimum, potential energy is maximum done clear
  B)
             Both kinetic and potential energies are maximum done clear
  C)
             Kinetic energy is maximum, potential energy is minimum done clear
  D)
             Both kinetic and potential energies are minimum done clear
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• question_answer21)
  Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing S.H.M. is                                                [CBSE PMT 2002]
  A)
             ? a done clear
  B)
             + a done clear
  C)
             \[\pm \,a\]                            done clear
  D)
             \[\pm \frac{a}{4}\] done clear
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• question_answer22)
  When a mass M is attached to the spring of force constant k, then the spring stretches by l. If the mass oscillates with amplitude l, what will be maximum potential energy stored in the spring                                              [BHU 2002]
  A)
             \[\frac{kl}{2}\]                      done clear
  B)
             \[2kl\] done clear
  C)
             \[\frac{1}{2}Mgl\]               done clear
  D)
             Mgl done clear
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• question_answer23)
  The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where E is the total energy)                                                             [CBSE PMT 2003]
  A)
             \[\frac{1}{8}E\]                    done clear
  B)
             \[\frac{1}{4}E\] done clear
  C)
             \[\frac{1}{2}E\]                    done clear
  D)
             \[\frac{2}{3}E\] done clear
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• question_answer24)
  A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement x. Which of the following statements is true                             [AIEEE 2003]
  A)
             P.E. is maximum when x = 0 done clear
  B)
             K.E. is maximum when x = 0 done clear
  C)
             T.E. is zero when x = 0 done clear
  D)
             K.E. is maximum when x is maximum done clear
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• question_answer25)
  If <E> and <U> denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is                                  [MP PMT 2004]
  A)
             <E> = <U>                              done clear
  B)
             <E> = 2<U> done clear
  C)
             <E> = ? 2<U>                        done clear
  D)
             <E>= ? <U> done clear
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• question_answer26)
  The total energy of a particle, executing simple harmonic motion is                                          [AIEEE 2004]
  A)
             \[\propto x\]                        done clear
  B)
             \[\propto {{x}^{2}}\]         done clear
  C)
             Independent of\[x\]         done clear
  D)
             \[\propto {{x}^{1/2}}\] done clear
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• question_answer27)
  The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the mass of the particle is 0.32 kg, then what is the maximum velocity of the particle [MH CET 2004]
  A)
             \[5m/s\]                                 done clear
  B)
             \[15m/s\] done clear
  C)
             \[10m/s\]                               done clear
  D)
             \[20m/s\] done clear
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• question_answer28)
  Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its                   (1)      Amplitude  (2)   Period      (3)  Displacement Of these statements                               [RPMT 2001; BCECE 2005]
  A)
             (1) and (2) are correct       done clear
  B)
             (2) and (3) are correct       done clear
  C)
             (1) and (3) are correct       done clear
  D)
             (1), (2)  and (3) are correct done clear
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• question_answer29)
  A particle starts simple harmonic motion from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is \[3E/4.\] Its displacement at that instant is [Kerala PET 2005]
  A)
             \[1/\sqrt{2}\]                             done clear
  B)
             \[a/2\] done clear
  C)
             \[\frac{a}{\sqrt{3/2}}\]            done clear
  D)
             \[a/\sqrt{3}\] done clear
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• question_answer30)
  A particle executes simple harmonic motion with a frequency \[f\]. The frequency with which its kinetic energy oscillates is  [IIT JEE 1973, 87; Manipal MEE 1995; MP PET 1997; DCE 1997; DCE 1999; UPSEAT 2000; RPET 2002; RPMT 2004; BHU 2005]
  A)
             \[f/2\]                                      done clear
  B)
             \[f\] done clear
  C)
             \[2f\]                                        done clear
  D)
             \[4f\] done clear
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• question_answer31)
  The amplitude of a particle executing SHM is made three-fourth keeping its time period constant. Its total energy will be                                                                                        [RPMT 2004]
  A)
             \[\frac{E}{2}\]                       done clear
  B)
             \[\frac{3}{4}E\] done clear
  C)
             \[\frac{9}{16}E\]                  done clear
  D)
             None of these done clear
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• question_answer32)
  A particle of mass m is hanging vertically by an ideal spring of force constant K. If the mass is made to oscillate vertically, its total energy is                                         [CPMT 1978; RPET 1999]
  A)
             Maximum at extreme position done clear
  B)
             Maximum at mean position done clear
  C)
             Minimum at mean position done clear
  D)
             Same at all position done clear
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• question_answer33)
  A body is moving in a room with a velocity of 20 m / s perpendicular to the two walls separated by 5 meters. There is no friction and the collisions with the walls are elastic. The motion of the body is                                               [MP PMT 1999]
  A)
             Not periodic                            done clear
  B)
             Periodic but not simple harmonic done clear
  C)
             Periodic and simple harmonic done clear
  D)
             Periodic with variable time period done clear
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• question_answer34)
  A body is executing Simple Harmonic Motion. At a displacement x its potential energy is \[{{E}_{1}}\] and at a displacement y its potential energy is \[{{E}_{2}}\]. The potential energy E at displacement \[(x+y)\] is  [EAMCET 2001]
  A)
             \[\sqrt{E}=\sqrt{{{E}_{1}}}-\sqrt{{{E}_{2}}}\]              done clear
  B)
             \[\sqrt{E}=\sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}\] done clear
  C)
             \[E={{E}_{1}}+{{E}_{2}}\] done clear
  D)
             \[E={{E}_{1}}+{{E}_{2}}\] done clear
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