Question

An object moving in simple harmonic motion has an amplitude of 0.02m and a maximum acceleration of 40m/s2 . what is the frequency of the system (in Hz)

Answer 1

Answer:

f = 7.11 Hz

Explanation:

Given that,

The amplitude of object in SHM, A = 0.02 m

The maximum acceleration of the object, a = 40 m/s²

We need to find the frequency of the system.

The maximum acceleration of the object in SHM is given by :

$a=\omega ^2 A$

Where $\omega$ is angular frequency

$\omega^2=\dfrac{a}{A}\\\\\omega=\sqrt{\dfrac{a}{A}} \\\\=\sqrt{\dfrac{40}{0.02}} \\\\\omega=44.721\ rad/s$

We know that,

$f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{44.721}{2\pi}\\\\f=7.11\ Hz$

So, the frequency of the system is 7.11 Hz.