Physics - Simple Harmonic Motion

Question - 1

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants \({ k }_{ 1 }\) and \({ k }_{ 2 }\) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that on N is 

  • A \(\frac { { k }_{ 1 } }{ { k }_{ 2 } } \)
  • B \(\sqrt { \frac { { k }_{ 1 } }{ { k }_{ 2 } } } \)
  • C \(\frac { { k }_{ 2 } }{ { k }_{ 1 } } \)
  • D \(\sqrt { \frac { { k }_{ 2 } }{ { k }_{ 1 } } } \)

Question - 2

A body is executing SHM with an amplitude of 0.1 m. Its velocity while passing through the mean position is 3m/s. Its frequency in Hz is 

  • A \(15\pi \)
  • B \(\frac { 15 }{ \pi } \)
  • C \(30\pi \)
  • D \(25\pi \)

Question - 3

Two particles are executing SHMs. The equations of their motions are 

\({ Y }_{ 1 }=10sin\left( \omega t+\frac { \pi }{ 4 } \right) \)

\({ Y }_{ 2 }=5sin\left( \omega t+\frac { \sqrt { 3 } \pi }{ 4 } \right) \)

What is the ratio of their amplitudes.

  • A 1:1
  • B 2:1
  • C 1:2
  • D None of these

Question - 4

What is the maximum acceleration of the particle doing the SHM?

\(Y=2sin\left[ \frac { \pi t }{ 2 } +\phi \right] \) where Y is in cm 

  • A \(\frac { \pi }{ 2 } cm/{ s }^{ 2 }\)
  • B \(\frac { { \pi }^{ 2 } }{ 2 } cm/{ s }^{ 2 }\)
  • C \(\frac { { \pi } }{ 4 } cm/{ s }^{ 2 }\)
  • D \(\frac { { { \pi }^{ 2 } } }{ 4 } cm/{ s }^{ 2 }\)

Question - 5

The amplitude and the time period in a SHM is 0.5 cm and 0.4 s respectively. If the initial phase is \(\frac { \pi }{ 2 } \) rad, then the equation of SHM will be 

  • A \(Y=0.5\quad sin\quad 5\pi t\)
  • B \(Y=0.5\quad sin\quad 4\pi t\)
  • C \(Y=0.5\quad sin\quad 2.5\pi t\)
  • D \(Y=0.5\quad cos\quad 5\pi t\)

Question - 6

A particle is executing simple harmonic motion with a period of T seconds and amplitude a meter. The shortest time it takes to reach a point \(\frac { a }{ \sqrt { 2 } } \) m from its mean position in seconds is 

  • A T
  • B \(\frac { T }{ 4 } \)
  • C \(\frac { T }{ 8 } \)
  • D \(\frac { T }{ 16 } \)

Question - 7

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

  • A \(\frac { T }{ 2 } \)
  • B \(\frac { T }{ 4 } \)
  • C \(\frac { T }{ 8 } \)
  • D \(\frac { T }{ 12 } \)

Question - 8

A particle executing SHM of amplitude 4 cm and T=4 s.The time taken by it to move from positive extreme position to half the amplitude is 

  • A 1 s
  • B \(\frac { 1 }{ 3 } \)s
  • C \(\frac { 2 }{ 3 } \)s
  • D \(\sqrt { \frac { 3 }{ 2 } } \) s

Question - 9

Two simple harmonic motions are represented by the equations \({ y }_{ 1 }=0.1\quad sin\left( 100\pi t+\frac { \pi }{ 3 } \right) \) and \({ y }_{ 2 }=0.1\quad cos\pi t\). The phase difference of velocity of particle 1 with respect to the velocity of particle 2 at time t=0 is 

  • A \(\frac { -\pi }{ 3 } \)
  • B \(\frac { \pi }{ 6 } \)
  • C \(\frac { -\pi }{ 6 } \)
  • D \(\frac { \pi }{ 3 } \)

Question - 10

A particle executing simple harmonic motion has an amplitude of 6 cm. Its acceleration at a distance of 2 cm from the mean position is 8 cm /\({ s }^{ 2 }\). The maximum speed of the particle is 

  • A 8 cm/s
  • B 12 cm/s
  • C 16 cm/s
  • D 24 cm/s
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