Question

Please help me with the following problem.

A single degree of freedom mechanical system has a response with time that is harmonic. Based on your experimental data, you determine that the response has an amplitude of 1 cm and a frequency of 10 Hz. Determine the natural period, maximum velocity, and maximum acceleration.

Answer 1

I've only been able to solve for the natural period.

\[\tau=\frac{ 1 }{ f }=\frac{ 1 }{ 10Hz }=0.1s\]

Answer 2

model the position using
\[ x= A \sin 2 \pi f \ t \]
with A= 1 cm and f= 10 Hz, you have
\[x = \sin 20 \pi t\]

Answer 3

as your "system" oscillates back and forth (with a center at x=0), it will be slowest at the "edges" (think of a swing going back and forth)
it will be fastest as it zooms by x=0

do you know calculus?
if so , you can find
\[ v= 20 \pi \cos(20 \pi t) \]
and at t=0 or 0.05 or 0.1 you will have a peak velocity \( \pm 20 \pi\ cm/s\)