JEE Main 2011 — Waves & Oscillations

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}$. This represents a

Two particles are executing simple harmonic motion of the same amplitude $\mathrm{A}$ and frequency $\omega$ along the $x$-axis. Their mean position is separated by distance $X_0\left(X_0>A\right)$. If the maximum separation between them is $\left(X_0+A\right)$, the phase difference between their motion is :

A mass $M$, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $\mathrm{m}$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is :