Answer: D(t) =
Explanation: A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:
y = or y =
where:
|a| is initil displacement
is period
For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:
or
For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:
period =
12 =
ω =
Replacing values:
The equation of displacement, D(t), of a spring with damping factor is .