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A ring of mass m is pivoted at a point on its periphery and free to oscillates in vertical plane. A particle of same mass is attached at the lowest point of the ring then time period of small oscillations is

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Important Questions on Oscillations

MEDIUM
Identify the function which represents a periodic motion
MEDIUM
The function sin2(ωt) represents
EASY
A particle is moving in a circle with uniform speed. Its motion is
MEDIUM
A body is moving in a room with a velocity of 20 m s-1 perpendicular to the two walls separated by 5 meters. There is no friction and the collisions with the walls are elastic. The motion of the body is:
EASY
The motion of a body which repeats itself after equal intervals of time is called:
 
EASY
The circular motion of a particle with constant speed is
EASY
Assuming all the surfaces to be smooth, find the time period of oscillation of the ball released from the top of the wedge.

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HARD
An ideal gas is enclosed in a vertical cylindrical container and supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. Atmospheric pressure is p0 and when the piston is in equilibrium, the volume of the gas is V0. The piston is now displaced slightly from its equilibrium position. Assuming that the system, is completely isolated from, its surroundings,  what is the frequency of oscillation.
EASY
The circular motion of a particle with constant speed is
MEDIUM
The displacement of a particle is represented by the equation y=sin3ωt. The motion is

 
MEDIUM
A particle moves in a circular path with a uniform speed. Its motion is,
MEDIUM
In a sonometer wire, the tension is maintained by suspending a mass M from free end of wire. The fundamental frequency of the wire is N Hz. If the suspended mass is completely immerged in water the fundamental frequency will
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
EASY
All oscillatory motions are necessarily periodic motions but:
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
MEDIUM
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is,
EASY
When a particle is moving with constant speed around a circular path the motion is
EASY
The time of reverberation of a room A is one second. What will be the time (in second) of reverberation of a room, having all the dimensions double of those of room A?
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
If the total energy of a simple harmonic oscillator is E, then its potential energy, when it is halfway to its endpoint will be