Question

Considering a damped spring-mass system released from rest with a positive initial displacement xo, resulting in a subsequent maximum positive displacement of xo/2. What is the damping ratio ζ of the system?

a) 0.25
b) 0.5
c) 0.75
d) 1.0

Answer 1

The damping ratio for a damped spring-mass system cannot be determined without the number of oscillations.

Step-by-step explanation:

The damping ratio for a damped spring-mass system can be calculated using the equation:

ζ = ln(Ai/A_f) / (2πn)

Where ζ is the damping ratio, Ai is the initial amplitude, A_f is the final amplitude, and n is the number of oscillations.

In this case, the initial amplitude is xo and the final amplitude is xo/2. Since the number of oscillations is not given, we cannot calculate the damping ratio.