A spring with a force constant of 1.50 N/m is attached to a mass of 120 g. The system has a damping constant of 0.0180 Ns/m. How long does it take the amplitude of the oscillations to decrease from 10.0 mm to 5.00 mm?
A) 12.5 s
B) 10.0 s
C) 6.25 s
D) 4.62 s
E) 9.24 s

Question

Quizplus · Accepted Answer

The amplitude of a damped harmonic oscillator decreases exponentially over time according to the formula A(t) = A_0 * e^(-bt/2m), where A_0 is the initial amplitude, b is the damping constant, m is the mass, and t is the time. Solving for t when A(t) = 5.00 mm, A_0 = 10.0 mm, b = 0.0180 Ns/m, and m = 0.120 kg gives approximately 9.24 s.

A Spring with a Force Constant of 1