Question

A particle moves along the X-axis according to the equation $x=10{\sin }^3\left(\pi t\right)$. the amplitudes and frequencies of component SHMs are

• A. $amplitude30/4,10/4;frequencies3/2,1/2$
• B. $amplitude30/4,10/4;frequencies1/2,3/2$
• C. $amplitude10,10;frequencies1/2,1/2$
• D. $amplitude30/4,10;frequencies3/2,2$

Answer 1

The correct option is C $amplitude10,10;frequencies1/2,1/2$

Given $x=10{sin}^3\left(\pi t\right)$

It is in the form $x=A{sin}^3\left(\omega t\right)$

where A= Amplitude. Here, A=10

We know that $w=2\pi f$

Here $2\pi f=\pi f=\frac{1}{2}$