a 1kg block is executing simple harmonic motion of amplitude 0.1m on a smooth horizontal surface under the restoring force of a spring of spring constant 100N/M.A block of mass 3kg is gently placed on it at the instant it passes through the mean position .Assuming that the two blocks move togther,find the frequency and the amplitude of the motion?

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  1. Before the 3 kg weight was added, the period was
    P = 2 pi sqrt(m/k) = 0.628 s.

    When you add 3 km, the total mass is quadrupled and the period is increased by a facgtor of sqrt4 = 2. The new period is

    P = 1.257 s.

    The new frequency is 1/P = 0.796 Hz

    With the mass added at the equilibrium position, the velocity instantly drops by a factor of 4 to preserve linerar momentum. The total kinetic energy at that point is then reduced by a factor (4/1)*(1/4)^2 = 1/4

    With the new reduced total energy, the pair of blocks can only have an amplitude sqrt (1/4) = 1/2 as large as before.

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