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 :
[tex]a=\omega ^2 A[/tex]
Where [tex]\omega[/tex] is angular frequency
[tex]\omega^2=\dfrac{a}{A}\\\\\omega=\sqrt{\dfrac{a}{A}} \\\\=\sqrt{\dfrac{40}{0.02}} \\\\\omega=44.721\ rad/s[/tex]
We know that,
[tex]f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{44.721}{2\pi}\\\\f=7.11\ Hz[/tex]
So, the frequency of the system is 7.11 Hz.
