Two simple harmonic motions are represented by equations y_1 = 4 … - Vidyadip

MCQ

Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?

A
$\phi $
B
$-\phi $
C
$\left( {\phi + \frac{\pi }{2}} \right)$
✓
$\left( {\phi - \frac{\pi }{2}} \right)$

✓

Answer

Correct option: D.

$\left( {\phi - \frac{\pi }{2}} \right)$

d
$y_{1}=4 \sin (10 t+\phi)$

$y_{2}=5 \cos 10 t$

$\Rightarrow \mathrm{y}_{2}=5 \sin \left(10 \mathrm{t}+\frac{\pi}{2}\right)$

phase difference $\frac{\pi}{2}-\phi$

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