Question

Two SHMs are represented by $y_1$ = A sin ($\omega$t + $\varphi$), $y_2$ = A/2 [sin $\omega$ t + $\sqrt{3}$ cos $\omega$t]. Find ratio of their amplitudes.

Answer 1

$y_2$ = A/2 [sin $\omega$t + $\sqrt{3}$cos $\omega$t] = A[1/2$\omega$t + $\sqrt{3}$/2cos $\omega$t]

= A [sin ($\pi$/3)cos $\omega$t + cos ($\pi$/3) $\omega$t]

$y_2$ = A sin ($\omega$t + $\pi$/3) and $y_1$ = A sin ($\omega$t + $\varphi$)

so, $A_1$/$A_2$ = 1