A 15.5 kg mass vibrates in simple harmonic motion with afrequency of 7.9 Hz. It

Question

A 15.5 kg mass vibrates in simple harmonic motion with afrequency of 7.9 Hz. It has a maximum displacement from equilibriumof +14 cm at time, t = 0.00 s. What is the position of the mass attime,    t = 0.35 s? And when an object vibrates in simple harmonic motion in thevertical direction, where does its minimum speed occur? (atthe highest endpoint, lowest endpoint, at both endpointsor at the equilibrium endpoint?) A 15.5 kg mass vibrates in simple harmonic motion with afrequency of 7.9 Hz. It has a maximum displacement from equilibriumof +14 cm at time, t = 0.00 s. What is the position of the mass attime,    t = 0.35 s? And when an object vibrates in simple harmonic motion in thevertical direction, where does its minimum speed occur? (atthe highest endpoint, lowest endpoint, at both endpointsor at the equilibrium endpoint?)

Explanation / Answer

f = 7.9 Hz, x(t) = 14 cos(2f*t) cm = 14cos(2*7.9*t) x(0.35) = 14 cos(2*7.9*0.35) cm = 1.32 cm v(t) = dx/dt = -14*2*7.9 sin(2*7.9*t) vmin = 0, 2*7.9*t = k   (k = 0, 1, 2, ...) t = k*(0.0633) s or t = 0.0633 s, 0.127 s, ...

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