Question

A particle is subjected to two SHMs one along the x-axis and the other on a line making an angle ${45}^{\circ }$ with the x-axis. The two motions are $x=x_0\sin \omega t$ and $p=p_0\sin \omega t$. Find their resultant amplitude.

• A. $x_0+p_0$
• B. $\sqrt{x_0^2+p_0^2+\sqrt{2}{x}_0{p}_0}$
• C. $\sqrt{x_0^2+p_0^2-\sqrt{2}{x}_0{p}_0}$
• D. $\sqrt{x_0^2+p_0^2}$

Answer 1

Answer: (B)

$\sqrt{x_0^2+p_0^2+\sqrt{2}{x}_0{p}_0}$

$A_{res}=\sqrt{x_0^2+p_0^2+2x_0{p}_0\cos 45}$
$\Rightarrow A_{res}=\sqrt{x_0^2+p_0^2+\sqrt{2}{x}_0{p}_0}$