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A particle performs simple harmonic motion. A large number of snapshots of its position are taken at random. A histogram of these positions will

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Important Questions on Oscillations

MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M

The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale) 

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Which of the following statements is/are true for this motion? 

(A) The force is zero at t=3T4
(B) The magnitude of acceleration is maximum at t=T
(C) The speed is maximum at t=T4
(D) The P.E. is equal to K.E. of the oscillation at t=T2

EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be:
HARD
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A piston is performing S.H.M. in the vertical direction with a frequency of 0.5 Hz. A block of 10 kg is placed on the piston. The maximum amplitude of the system such that the block remains in contact with the piston is
HARD
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle executes simple harmonic motion with an amplitude of 5cm . When the particle is at 4cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A simple pendulum oscillates harmonically about x=0 with an amplitude A and time period T. Its speed at x=A/2 is
HARD
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle is performing a linear simple harmonic motion of amplitude A. When it is midway between its mean and extreme position, the magnitudes of its velocity and acceleration are equal. What is the periodic time of the motion?
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle executes S.H.M., the graph of velocity as a function of displacement is :
MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance 2A3 from equilibrium position. The new amplitude of the motion is:
MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle performs S.H.M. with amplitude A. Its speed is tripled at the instant when it is at a distance of 2A3 from the mean position. The new amplitude of the motion is
HARD
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle performs linear SHM. At a particular instant, the velocity of the particle is u and acceleration is α (both having the same direction). At another instant velocity is v and acceleration is  β 0<α<β (both in opposite direction to each other).The distance between the two positions is
MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M

In case of a simple harmonic motion, if the velocity is plotted along the X -axis and the displacement (from the equilibrium position) is plotted along the Y -axis, the resultant curve happens to be an ellipse with the ratio:
 major axis along X minor axis along Y=20π

What is the frequency of the simple harmonic motion?

MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:
MEDIUM
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A body undergoing simple harmonic motion has a maximum acceleration of 8 m s-2 and maximum speed of 1.6 m s-1. What is the time period T ?
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle executing S.H.M. has velocities v1 and v2 at distance x1 and x2 respectively from mean position. The angular velocity ω of the particle is given by
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
The oscillation of a body on a smooth horizontal surface is represented by the equation, X=Acos⁡ωt, where X= displacement at time t, ω=  frequency of oscillation, a= acceleration at time t and T= time period.
Which one of the following graph shows correctly the variation a with t ?
HARD
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s-1. At, t=0 the displacement is 5 m. What is the maximum acceleration? The initial phase is π4 .
EASY
Physics>Waves and Oscillations>Oscillations>Differential Equation of Linear S.H.M
A particle is executing SHM along a straight line. Its velocities at distances x1 and x2 from the mean position are V1 and V2 respectively. Its time period is: