Question

A particle moves along y-axis according to the equation y (in cm)$=3\sin 100\pi t+8{\sin }^{2}50\pi t-6$

• A. the particle performs SHM
• B. the amplitude of the particle's oscillation is 5 cm
• C. the mean position of the particle is at y=- 2 cm
• D. the particle does not perform SHM

Answer 1

Answer: (A), (B), (C)

the mean position of the particle is at y=- 2 cm
the particle performs SHM
the amplitude of the particle's oscillation is 5 cm

The given equation can be written as
$y=3\sin 100\pi t+(4-4\cos 100\pi t)-6$
$=3\sin 100\pi t+4\sin (100\pi t+\pi \pi /2)-2$
or $y=5\sin (100\pi -{53}^{\circ })-2$
$y_{max}=5-2=3$
$y_{min}=-5-2=-7$
Mean position$=\frac{y_{max}+y_{min}}{2}=-2$ cm