I was wondering if someone could please help me out with thisproblem: The 15 g h

Question

I was wondering if someone could please help me out with thisproblem:
The 15 g head of a bobble-head doll oscillates in simpleharmonic motion at a frequency of 4.0 Hz. a) What is the spring constant of the spring on which the headis mounted? b) Suppose the head is pushed 2.0 cm against the spring, thenreleased. What is the head’s maximum speed as it oscillates? c) The amplitude of the head’s oscillations decreases to0.5 cm in 4.0 s. What is the head’s damping constant? I was wondering if someone could please help me out with thisproblem:
The 15 g head of a bobble-head doll oscillates in simpleharmonic motion at a frequency of 4.0 Hz. a) What is the spring constant of the spring on which the headis mounted? b) Suppose the head is pushed 2.0 cm against the spring, thenreleased. What is the head’s maximum speed as it oscillates? c) The amplitude of the head’s oscillations decreases to0.5 cm in 4.0 s. What is the head’s damping constant?

Explanation / Answer

m = 15 g, f = 4.0 Hz a) = 2f = (k/m) k = m*(2f)2 = 9.475 N/m b) A = 2.0 cm v = A = A(k/m) = 0.503 m/s c) 0.5 = 2.0 e-*4.0 = ln(4)/4 =0.3466 the damping constant b = 2m = 0.0104 kg/s

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