JEE Main & Advanced Physics Simple Harmonic Motion Question Bank

done Superposition of S H M and Resonance Total Questions - 14

• question_answer1)
  The S.H.M. of a particle is given by the equation\[y=3\sin \omega \,t+4\cos \omega \,t\]. The amplitude is          [MP PET 1993]
  A)
             7     done clear
  B)
             1 done clear
  C)
             5     done clear
  D)
             12  done clear
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• question_answer2)
  If the displacement equation of a particle be represented by \[y=A\sin PT+B\cos PT\], the particle executes       [MP PET 1986]
  A)
             A uniform circular motion done clear
  B)
             A uniform elliptical motion done clear
  C)
             A S.H.M. done clear
  D)
             A rectilinear motion done clear
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• question_answer3)
  The motion of a particle varies with time according to the relation  \[y=a(\sin \omega \,t+\cos \omega \,t)\], then
  A)
             The motion is oscillatory but not S.H.M. done clear
  B)
             The motion is S.H.M. with amplitude a done clear
  C)
             The motion is S.H.M. with amplitude \[a\sqrt{2}\] done clear
  D)
             The motion is S.H.M. with amplitude \[2a\] done clear
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• question_answer4)
  The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by \[\frac{\pi }{2}\] is [BHU 2003; CPMT 2004; MP PMT 1989, 2005; BCECE 2005]
  A)
             Simple harmonic                 done clear
  B)
             Circular done clear
  C)
             Elliptical                                   done clear
  D)
             Parabolic done clear
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• question_answer5)
  The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of \[\pi \] results in the displacement of the particle along                                     [CBSE PMT 1990]
  A)
             Straight line                           done clear
  B)
             Circle done clear
  C)
             Ellipse                                      done clear
  D)
             Figure of eight done clear
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• question_answer6)
  Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be [MP PMT 1992]
  A)
             A circle                                     done clear
  B)
             An ellipse done clear
  C)
             A straight line                       done clear
  D)
             A parabola done clear
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• question_answer7)
  The displacement of a particle varies according to the relation x = 4(cospt + sinpt). The amplitude of the particle is                                                                                               [AIEEE 2003]
  A)
             8     done clear
  B)
             ? 4 done clear
  C)
             4     done clear
  D)
             \[4\sqrt{2}\] done clear
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• question_answer8)
  A S.H.M. is represented by \[x=5\sqrt{2}(\sin 2\pi t+\cos 2\pi t).\]The amplitude of the S.H.M. is                                                 [MH CET 2004]
  A)
             10 cm                                       done clear
  B)
             20 cm done clear
  C)
             \[5\sqrt{2}\]cm                    done clear
  D)
             50 cm done clear
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• question_answer9)
  Resonance is an example of       [CBSE PMT 1999; BHU 1999; 2005]
  A)
             Tuning fork                            done clear
  B)
             Forced vibration done clear
  C)
             Free vibration                       done clear
  D)
             Damped vibration done clear
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• question_answer10)
  In case of a forced vibration, the resonance wave becomes very sharp when the                              [CBSE PMT 2003]
  A)
             Restoring force is small done clear
  B)
             Applied periodic force is small done clear
  C)
             Quality factor is small done clear
  D)
             Damping force is small done clear
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• question_answer11)
   Amplitude of a wave is represented by                    \[A=\frac{c}{a+b-c}\]            Then resonance will occur when                                                    [CPMT 1984]
  A)
             \[b=-c/2\]                              done clear
  B)
             b = 0 and a = ? c                   done clear
  C)
             \[b=-a/2\]                              done clear
  D)
             None of these done clear
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• question_answer12)
  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 is maximum for \[\omega ={{\omega }_{2}}\], then (where w0 natural frequency of oscillation of particle)                                                                      [CBSE PMT 1998]
  A)
             \[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{o}}\] done clear
  B)
             \[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}={{\omega }_{o}}\] done clear
  C)
             \[{{\omega }_{1}}\ne {{\omega }_{0}}\] and \[{{\omega }_{2}}={{\omega }_{o}}\] done clear
  D)
             \[{{\omega }_{1}}\ne {{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{o}}\] done clear
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• question_answer13)
  A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to                                                                        [AFMC 2003; JIPMER 1999]
  A)
             Air friction done clear
  B)
             Moment of inertia done clear
  C)
             Weight of the bob done clear
  D)
             Combination of all the above done clear
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• question_answer14)
  A simple pendulum oscillates in air with time period T and amplitude A. As the time passes                          [CPMT 2005]
  A)
             T and A both decrease done clear
  B)
             T increases and A is constant done clear
  C)
             T increases and A decreases done clear
  D)
             T decreases and A is constant done clear
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