Question

Two simple harmonic motions are represented by equations $y_{1}=4 \sin (10 t+\phi) \Rightarrow y_{2}=5 \cos 10 t$ What is the phase difference between their velocities?

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

Answer 1

Answer: (D)

$y_1 = 4\,\sin(10\,t + \phi)$
$y_2 = 5\,\cos\,10 t$
$v_1 = \frac{dy_1}{dt} = 40\,\cos(10 t + \phi)$
$v_2 = \frac{dy_2}{dt} = -50\, \sin\,10t$
$ = 50\,\cos(10t + \pi/2)$
Phase difference between $v_1$ and $v_2 = \,\cos(10t + \pi/2)$