Question

An instantenous displacement of a simple harmonic oscillator is $x=A\cos (\omega t+\frac{\pi }{4})$ . Its speed will be maximum at time:

• A. $\frac{\pi }{4\omega }$
  
• B. $\frac{\pi }{2\omega }$
  
• C. $\frac{\pi }{\omega }$
  
• D. $\frac{2\pi }{\omega }$
  

Answer 1

The correct option is A $\frac{\pi }{4\omega }$

displacement of oscillator : $x=A\cos (wt+\frac{\pi }{4})$ so speed of oscillator.

$V=\frac{dx}{dt}{=}^{(-)}Aw\sin (wt+\frac{\pi }{4})$

Speed would maximum when $\frac{dv}{dt}=0$ at time t.

$\Rightarrow -A{w}^2\cos (wt+\frac{\pi }{4})$

$\Rightarrow \cos (wt+\frac{\pi }{4})=0$

$\Rightarrow wt+\frac{\pi }{4}=\frac{\pi }{2}\Rightarrow t=\frac{\pi }{4w}$