### Find the angular frequencies of the constituent oscillations

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Q1. A particle performs harmonic oscillations along the x axis about the equilibrium position x = 0. The oscillation frequency is ω = 4.00 s-1. At a certain moment of time the particle has a coordinate x0 = 25.0 cm and its velocity is equal to vx0 = 100 cm/s. Find the coordinate x and the velocity vx of the particle t = 2.40 s after that moment.

Q2. The superposition of two harmonic oscillations of the same direction results in the oscillation of a point according to the law x = a cos (2.1t) cos (50.0t), where t is expressed in seconds. Find the angular frequencies of the constituent oscillations and the period with which they beat.

Q3. A ball is suspended by a thread of length l at the point O on the wall, forming a small angle α with the vertical (Fig.). Then the thread with the ball was deviated through a small angle β (β > α) and set free. Assuming the collision of the ball against the wall to be perfectly elastic, find the oscillation period of such a pendulum.

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