Question

The equation of the displacement of two particles making SHM are represented by

$y_1$ = a sin $(\omega t+\varphi )$ & $y_2$ = a cos $\left(\omega t\right)$.

The phase difference of the velocities of the two particles is :

• A. $\frac{\pi }{2}+\varphi$
• B. $-\varphi$
• C. $\varphi$
• D. $\varphi -\frac{\pi }{2}$

Answer 1

Answer: (D)

$\varphi -\frac{\pi }{2}$

$y_1=asin(\omega t+\varphi )$
$y_2=acos\left(\omega t\right)$
$y_1=a\omega cos(\omega t+\varphi )=a\omega sin(\omega t+\varphi +\pi {/}_2)$
$y_2=-a\omega sin\left(\omega t\right)=a\omega sin(\pi +\omega t)$
therefore phase difference$=\omega t+\varphi +\pi {/}_2-(\pi +\omega t)$
$=\varphi -\pi {/}_2$