Question

Help

The 12 g head of a bobble head doll oscillates in SHM at a frequency of 5 9 Hz Significant Figures Feedback: Your answer 16.49092 N/m was either rounded differently or used a different number of significant figures than required for this Suppose the head is pushed 2 0 cm against the spring then released The amplitude of the head's oscillations decreases to 0.5 cm in 4.0 s What is the head's damping constant? Express your answer using two significant figures.

Answer 1

w = 2 pi f = sqrt [k / m]

k = m * (2 pi f)² = 12 * 10^-3 * (2 pi * 5.9)²= 16.49 N/m

v = w A = x_m * sqrt [k / m] = 0.02 * sqrt [16.49 / 12 * 10^-3] = 0.741 m/s

x(t) = x_m * e^-bt/2m

0.005 = 0.02 * e^-bt/2m

e^-bt/2m = 0.25

-bt/2m = ln (0.25) = -1.386

-b(4.0 s) / (2 * 0.012) =  -1.386

b = 8.316 * 10^-3 kg/s