The relation between acceleration and displacement of four particles are given below: (a) $a_x = +5x$. (b) $a_x= + 5x^2$. (c) $a_x = – 5x$ (d) $a_x= – 5x^2$. Which one of the particles is executing simple harmonic motion?
  • (a)
  • (b)
  • (c)
  • (d)
For a particle executing SHM,four statement are made (i).Acceleration is proportional to the displacement in the direction of the motion (ii).Acceleration is proportional to the displacement but in opposite direction of the motion (iii). Total energy of particle remains constant (iv), KE and PE of particle remains constant Which of the following is correct?
  • (i) only
  • (ii) and (iii) only
  • (iii) and (iv) only
  • (iv) only
If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will
  • decrease
  • remain the same
  • increase
  • First increase and then decrease
The length of the simple pendulum is increased by 69%. What is the percentage increase in its timeperiod?
  • 69%
  • 10%
  • 20%
  • 30%
The displacement of a particle varies with time according to the relation $y = a sin \omega t + b cos \omega t$
  • The motion is oscillatory but not S.H.M
  • The motion is S.H.M. with amplitude a + b
  • The motion is S.H.M. with amplitude $a^2 + b^2$.
  • The motion is S.H.M. with amplitude $\sqrt {a^2 + b^2}$ .
The total energy of a particle executing simple harmonic motion is proportional to
  • displacement from equilibrium position
  • frequency of oscillation
  • velocity of equilibrium position
  • square of amplitude of motion
The amplitude and phase of a particle executing SHM depends on
  • The displacement of particle at t=0
  • The velocity of particle at t=0
  • Both Velocity and displacement at t=0
  • Neither velocity and displacement at t=0
The bob A of a simple pendulum is released when the string makes an angle 45° with the vertical. Its hit another bob B of the same material and same mass kept at rest on the table. If the collision is elastic
  • B moves first and A follows it with half of its initial velocity
  • A comes to rest and B moves with the velocity of A
  • Both A and B moves with same velocity of A
  • Both A and B comes to rest at
Four statement are made about SHM (i). Maximum value of velocity in SHM is A2ω (ii). In SHM velocity of the particle is maximum when displacement is maximum (iii). Velocity of the particle is zero in SHM when displacement attains its maximum on either side (iv). Velocity in SHM vary periodically with time which of the following is correct?
  • (i) only
  • (ii) and (iii) only
  • (iii) and (iv) only
  • (iv) only
Angular frequency of system executing SHM depends on
  • mass
  • total energy
  • Force constant
  • Both mass and force constant
A simple pendulum consists of a mass attached to a light string l. if the system is oscillating through small angles which of the following is true
  • The frequency is independent of the acceleration due to gravity g
  • The period depends on the amplitude of the oscillation
  • The period is independent of mass m
  • the period is independent of length l
To execute SHM system must have
  • Elasticity
  • Moment of Inertia
  • Inertia
  • both Elasticity and Inertia
A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of $60 \ cm/s^2$. The period of oscillation is
  • $\pi$ s
  • $\frac {\pi}{2}$ s
  • $2\pi$ s
  • $\frac {\pi}{4}$ s
Four statement are made for SHM (i). Amplitude and initial displacement of particle in SHM are always equal (ii). Amplitude and initial displacement of particle in SHM are never equal (iii). Amplitude of a particle in SHM can be equal to its initial displacement (iv). Amplitude of a particle in SHM can be greater to its initial displacement which of the following is correct?
  • (i) only
  • (i) and (iii) only
  • (iii) and (iv) only
  • (iv) only
On a planet a freely falling body takes 2 sec when it is dropped from a height of 8 m, the time period of simple pendulum of length 1 m on that planet is
  • 3.14 sec
  • 6.28 sec
  • 1.67 sec
  • 9.42 sec
A particle of mass m is attached to a mass less string of length L and is oscillating in vertical plane with one end of string fixed to rigid support. Tension in the string at a certain instant is T=kmg. Then
  • K can never be equal to 1
  • K can never be greater than 1
  • K can never be greater than 3
  • K can never be less than 1
0 h : 0 m : 1 s

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