EASY
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The motion of a body along the same path is called oscillatory motion. (To-and-fro / Static)

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Important Questions on Oscillations

HARD
The potential energy of a particle of mass m executing s.h.m. along the X-axis is given byU=U0U0cos αx , where α is a constant. Find the period of oscillation for small x
 
EASY

A mass m is suspended by means of two coiled springs which have the same length in unstretched condition, as shown in figure. Their force constants are k1 and k2, respectively. When set into vertical vibrations, the period will be

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MEDIUM
Two masses m1 and m2 suspended together by a massless spring of spring constant K. When the masses are in equilibrium, m1 is removed without disturbing the system. The angular frequency of m2 is
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HARD

A highly rigid cubical block A of small mass M and side L is fixed rigidly on to another cubical block B of the same dimensions and of low modulus of rigidity η such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time-period of which is given by

EASY

A particle is undergoing simple harmonic motion. The graph shows variation of velocity of particle with its position from mean position. The frequency of simple harmonic motion is,

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HARD

A wooden Cube (density of wood d) of side 1 floats in a liquid of density ρ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period T, then T is given by

MEDIUM
The equation of motion of a particle is x=a cos(αt)2.The motion is
HARD
An air chamber of volume V has a neck of cross-sectional area a into which a light ball of mass m just fits and can move up and down without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air is B, the time period of the oscillation of the ball is
MEDIUM
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
EASY
A particle executing SHM crosses points A and B with the same velocity. Having taken 3s in passing from A to B, it returns to B after another 3s. The time period is
EASY
The circular motion of a particle with constant speed is
EASY
A particle executes simple harmonic oscillation with an amplitude A. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
MEDIUM
Two equal charges q are kept fixed at -a and +a along the x-axis. A particle of mass m and charge q2 is brought to the origin and given a small displacement along the x-axis, then
EASY

In the figure shown, the time period and the amplitude, respectively, when mass m is released from rest and when the spring is relaxed are (The inclined plane is smooth)

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MEDIUM
The time period of a particle in SHM depends, in general, on force constant and _____ but is independent of total energy or initial phase.
MEDIUM
The rotation of earth about its axis is
 
EASY
If the total energy of a simple harmonic oscillator is E, then its potential energy, when it is halfway to its endpoint will be
MEDIUM
The displacement of a particle is represented by the equation y=sin3ωt. The motion is