Question 349: Oscillations

Question

Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is $$\sqrt{2}$$ a. The initial phase difference between them is
$$\left[\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}\right]$$

Accepted Answer

$$x=x_1+x_2=A \sin (\omega t+\alpha)$$
Maximum value of $$x_1+x_2=A=\sqrt{2} a$$
$$\begin{aligned}
& A^2=a^2+a^2+2 a^2 \cos \alpha=2 a^2(1+\cos \alpha) \
& 	herefore 2 a^2=2 a^2(1+\cos \alpha) \quad 	herefore 1=1+\cos \alpha \
& 	herefore \quad \cos \alpha=0 \quad 	herefore \alpha=\frac{\pi}{2}
\end{aligned}$$

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{2}$$

Answer

zero

Answer

$$\frac{\pi}{3}$$

Oscillations

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