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A sphere of mass M and radius R is on a smooth fixed inclined plane in equilibrium as shown in the figure. If now the sphere is displaced through a small distance along the plane, what will be the angular frequency (in rads-1 of the resulting SHM? (Given, k=4M3 )

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Important Questions on Linear and Angular Simple Harmonic Motion

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Physics
IMPORTANT
If x,v and a  denote the displacement, the velocity and the acceleration of a particle executing SHM, of time period T, then, which of the following does not change with time?
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Physics
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A mass M, attached to a horizontal spring, executes s.h.m. with amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of A1A2 is
 
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Physics
IMPORTANT
Two particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x-axis. Their mean position is separated by distance x0x0>A. If the maximum separation between them is x0+A, the phase difference between their motion is
MEDIUM
Physics
IMPORTANT

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s. In another 10 s it will decrease to α times its original magnitude, where α equals

HARD
Physics
IMPORTANT
A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest, it travels a distance a, and in next τ s, it travels 2a in same direction, then:
 
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Physics
IMPORTANT
For a simple pendulum, a graph is plotted between its kinetic energy KE and potential energy PE against its displacement d. Which one of the following represents these correctly? (Graphs are schematic and not drawn to scale)
MEDIUM
Physics
IMPORTANT
A particle is executing simple harmonic motion with a time period T. At time t= 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like,
MEDIUM
Physics
IMPORTANT

The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t=43 s is

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