A mass m=4.5 kg is attached to the vertical spring with k=200 N/m and is set int

Question

A mass m=4.5 kg is attached to the vertical spring with k=200 N/m and is set into motion. Question: What is the frequency of the oscillation? If the amplitude of the oscillation is 3.5 cm, what is the maximum value of the velocity?

Explanation / Answer

a )The frequency of the oscillations is given by: f = 1/2p v(k/m) = 1/2p v(204/4.5) = 1.07 Hz b) v = A ? cos(? t + f) When cos(? t + f) = 1 => v = v_max v_max = A ? = 0.037 2p/f = 0.037 * 5.87= 0.22 m/s c) x = A sin(? t + f) ? t1 + f = arcsin(x1/A) ? t2 + f = arcsin(x2/A) ? (t2 – t1) = arcsin(x2/A) – arcsin(x1/A) ?t = 1/? (arcsin(x2/A) – arcsin(x1/A) ) ?t = f /2p (arcsin(2.5/0.037) – arcsin(1.5/0.037) ) ?t = 1.07/2p (arcsin(2.5/3.7) – arcsin(1.5/3.7) ) = 0.11 s d) v_max = A ? A = v_max/? = 45/ 5.87 = 7.66 m

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