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)

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