Question

The displacement of a moving particle is described by equation $y=0.4\left({\cos }^2\frac{\pi t}{4}-{\sin }^2\frac{\pi t}{4}\right)$ the motion of particle:

• A. is oscillatory but not $SHM$
• B. is $SHM$ of amplitude $0.4$
• C. is $SHM$ of amplitude $0.4/\sqrt{2}$
• D. is $SHM$ of amplitude $0.8$

Answer 1

Answer: (B)

is $SHM$ of amplitude $0.4$

$y=0.4({\cos }^2\frac{\pi t}{4}-{\sin }^2\frac{\pi t}{4})$

$y=0.4\left(\cos \frac{2\pi t}{4}\right)$

$y=0.4\left(\cos \frac{\pi t}{2}\right)$

$y=0.4\left(\sin [\frac{\pi }{2}-\frac{\pi t}{2}]\right)$

$y=0.4\left(\sin \frac{\pi (1-t)}{2}\right)$

We know equation of SHM is

$y=A\sin \omega t$

So, It is SHM with $A=0.4$

So, $Ans=B$