Question

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

• A. amplitude $30/4,10/4$; frequencies $3/2,1/2$
• B. amplitude $30/4,10/4$; frequencies $1/2,3/2$
• C. amplitude 10,10 ; frequencies $1/2,1/2$
• D. amplitude $30/4,10$; frequencies $3/2,2$

Answer 1

Answer: (B)

$x=10{\sin }^3(\pi t)$
$=10\sin \pi \left(\frac{1-\cos 2\pi t}{2}\right)$
$5\sin \pi t-5\sin \pi t\cos 2\pi t$
$5\sin \pi t-\frac{5}{2}\sin 3\pi t+\frac{5}{2}\sin \pi t$
$\frac{30}{4}\sin \pi t-\frac{5}{2}\sin 3\pi t$