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A cart of mass M that can slide on frictionless rails has a pendulum bob of mass m connected to it through a massless inextensible string. The cart can move only longitudinally on the rails. The ratio of time periods T2T1, when the pendulum swings in the vertical planes parallel and perpendicular to the rails is

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Important Questions on Oscillations

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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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A box placed on a smooth inclined plane is free to move. Find the time period of oscillation of the simple pendulum attached to the ceiling of the box.
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A ball suspended by a thread of length L at a point O on the wall forms a small angle α with the vertical. Then, the thread with the ball is deviated through a small angle β>α and set free. Assuming the collision of the ball with the wall as elastic, find the time period of oscillation of such a pendulum.
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In case of a mechanical wave, a particle oscillates, During oscillation, its kinetic and potential energy changes.  When particle is passing through mean position,