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Important Questions on Oscillations

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A particle P is moving on a circular path of radius R as shown in figure. If time period is 2 minutes, then the equation of projection on y axis for particle P is (where t is in seconds)
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The shortest distance travelled by a particle executing SHM from extreme position in 3 seconds is equal to half of its amplitude. The time period of given particle is
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A particle executes SHM about x=0 along x-axis. The equation for SHM is x=(10 cm)sinπ2t, where x is in cm and t is in seconds. The maximum speed of particle is 
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A block of mass m is suspended from a massless spring of spring constant 2k3 as shown in figure. If block of mass m is slightly displaced vertically downward and released, then it executes SHM. The time period of block is
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Figure shows the velocity-time graph of an object executing SHM. The correct equation for displacement - time (x-t) representing this motion is
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A particle of mass 1 kg is executing oscillation and its equation of motion is given by 2d2xdt2+dxdt+x=0. The motion is
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The circular motion of a particle with constant speed is
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If effective length of a simple pendulum is equal to radius of earth (R), time period will be