EASY
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What is the initial phase in Simple Harmonic Motion ?

Important Questions on Oscillations

HARD
A particle performs SHM along a straight line. In the first second, starting from rest at extreme position, it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the SHM is
MEDIUM
A particle executes simple harmonic motion between x=-A and x=+A. If it takes a time T1 to g0 from x=0 to x=A/2 and T2 to go from x=A/2 to x=A. Then
EASY
Which of the following equation represents a simple harmonic motion? (ω is angular frequency, A is amplitude of oscillation and i=-1)
HARD
A particle executes simple harmonic motion represented by displacement function as x(t)=Asin(ωt+ϕ). If the position and velocity of the particle at t=0 s are 2 cm and 2ω cm s-1 respectively, then its amplitude is x2 cm where the value of x is
EASY
A particle is performing SHM starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of
MEDIUM
The velocity and acceleration of a particle performing simple harmonic motion have a steady phase relationship. The acceleration shows a phase lead over the velocity in radians of
EASY
A particle of mass 0.1 kg is executing simple harmonic motion of amplitude 0.1 m. When the particle passes through the mean position, its kinetic energy is 8×10-3 J. If the initial phase is 45°, the equation of its motion is (Assume, x t as the position of the particle at time t)
MEDIUM
Define linear S.H.M.Obtain differential equation of linear S.H.M.
MEDIUM

The position co-ordinates of a particle moving in a 3D coordinate system is given by

x=acosωt

y=asinωt

and z=aωt

The speed of the particle is:

EASY
Which of the following plots represents schematically the dependence of the time period of a pendulum if measured and plotted as a function of its oscillations? (Note: amplitude need not be small)
HARD

The motion of a mass on a spring, with spring constant K is as shown in figure.

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The equation of motion is given by, x(t)=Asinωt+Bcosωt with ω=Km.
Suppose that at time t=0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t)=Ccos(ωt-ϕ), where C and ϕ are 

EASY
A simple pendulum of length L has mass M and it oscillates freely with amplitude A. At the extreme position, its potential energy is (g = acceleration due to gravity)
MEDIUM
Two simple harmonic motions are represented by the equations x1=5sin2πt+π4 and x2=52(sin2πt+cos2πt). The amplitude of the second motion is _____ times the amplitude in the first motion.
MEDIUM

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x0, from the block. The spring is then compressed by 2x0 and released. The time taken by the block to strike the other wall is

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HARD
From differential equation of linear S.H.M., obtain an expression for acceleration, velocity and displacement of a particle performing S.H.M.
EASY
Which one of the following expressions does not represent simple harmonic motion (SMH)?
EASY
The phase difference between the displacement and velocity of a particle executing simple harmonic motion is
EASY
If the differential equation for a simple harmonic motion is d2ydt2+2y=0, the time period of the motion is,
EASY
The weight suspended from a spring oscillates up and down. The acceleration of weight will be zero at
EASY
A particle of mass m is moving along the x-axis under the potential  V(x)= k x 2 2 + λ x  where k and  x are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency ω given by