Question

A simple harmonic oscillator has an amplitude of 0.17 m and a period of 0.84 s.
Determine the frequency, and the angular frequency of the motion. Write expressions for
the time dependence of displacement, velocity and acceleration. What are the maximum
values of the velocity and acceleration?

Answer 1

Question 23049

$$A = 0.17\,m, T = 0.84\,s.$$

The frequency, by definition $\nu = \frac{1}{T} = \frac{1}{0.84\,s} \approx 1.2\,s^{-1}$ .

The angular frequency is by definition, $\omega = \frac{2\pi}{T} = 7.48\,s^{-1}$ .

General expression for displacement

$$x = A \sin (\omega t + \delta), \quad v = \dot{x} = A \omega \cos (\omega t + \delta), \quad a = \dot{v} = -A \omega^2 \sin (\omega t + \delta).$$

Maximum values for displacement, velocity and acceleration are 0.17; 1.27; 9.51 respectively.