Question

The amplitude of SHM $y=2(\sin 5\pi t+\sqrt{2}\cos \pi t)$ is

• A. $2$
• B. $2\sqrt{2}$
• C. $4$
• D. $2\sqrt{3}$

Answer 1

Answer: (D)

$2\sqrt{3}$

Answer 2

The equation of SHM is
$y=A\sin (\omega t+\phi )$
Or $y=A(\sin \omega t\cos \phi +\cos \omega t\sin \phi )$ ... (i)
The given expression is $y=2(\sin 5\pi t+\sqrt{2}\cos \pi t)$ ...(ii)
$A\cos \phi =2$ and $A\sin \phi =2\sqrt{2}$
Squaring and adding, we get $A=2\sqrt{3}$