Question

A particle is executing $SHM$ about $y=0$ along $y-$axis. Its position at an instant is given by $y\left(m\right)=5(sin3\pi t+\sqrt{3}cos3\pi t).$ The amplitude of oscillation is

• A. $10m$
• B. $5m$
• C. $5(1+\sqrt{3})m$
• D. $5\sqrt{3}m$

Answer 1

The correct option is A $10m$

$y\left(m\right)=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)y\left(m\right)=5\times 2(\frac{1}{2}\times \sin 3\pi t+\frac{1}{2}\times \sqrt{3}\cos 3\pi t)y\left(m\right)=10(\cos \frac{\pi }{3}\times \sin 3\pi t+\sin \frac{\pi }{3}\times \cos 3\pi t)y\left(m\right)=10\sin (3\pi t+\frac{\pi }{3})$

So, amplitude of oscillation is 10.