Question

# The periodic time of a body executing simple harmonic motion is $$3$$ sec. After much interval form time $$t=0$$, its displacement will be half of its amplitude.

A
18sec
B
16sec
C
14sec
D
13sec

Solution

## The correct option is C $$\dfrac 14 sec$$Given that, time period $$T= 3seconds$$.The equation for SHM is given by, $$y=Asin \omega t$$ and $$\omega = 2\pi f=\frac{2\pi}{T}$$Let after time $$t=t$$, the displacement is half its amplitude, $$\Rightarrow \frac{A}{2}=Asin(\frac{2\pi}{3}t)$$$$\Rightarrow sin(\frac{\pi}{6})= sin(\frac{2\pi t}{3})$$$$\Rightarrow \frac{\pi}{6}=\frac{2\pi t}{3}$$or, $$t=\frac{1}{4} sec$$ is our required answer.Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More