The maximum speed at which a patch of the surface moves during a vibration is 4.5 m/s . What is the amplitude of the vibration, assuming it to be simple harmonic motion?

a) Angular frequency, w = 0.0184 rad/s

b) Amplitude of vibration = 245 m

Explanation:

a) Angular frequency, w = 2πf

f = 1/T, T = 5.7 minutes = 5.7 × 60 = 342 s

f = 1/342 = 0.00292 Hz or 0.00292/s

w = 2π (0.00292) = 0.0184 rad/s

b) Amplitude of simple harmonic motion,

displacement of simple harmonic motion, x(t) = A cos (wt-Φ)

A = amplitude

v = dx/dt = - Aw (sin (wt - Φ)

Velocity amplitude of simple harmonic motion = Amplitude × angular frequency

Amplitude = (velocity amplitude)/(angular frequency) = 4.5/0.0184 = 245m

Hope this Helps!!!

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