JEE Main 2003 — Waves & Oscillations

A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement $x$. Which of the following statements is true?

A mass $\mathrm{M}$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by $\mathrm{m}$, the time period becomes $\frac{5 \mathrm{~T}}{3}$. Then the ratio of $\frac{\mathrm{m}}{\mathrm{M}}$ is

A tuning fork of known frequency $256 \mathrm{~Hz}$ makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

The displacement of a particle varies according to the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is

The displacement $y$ of a wave travelling in the $x$-direction is given by $y=10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right)$ metres where $\mathrm{x}$ is expressed in metres and $\mathrm{t}$ in seconds. The speed of the wave-motion, in $\mathrm{ms}^{-1}$, is

Two particles $\mathrm{A}$ and $\mathrm{B}$ of equal masses are suspended from two massless springs of spring constant $\mathrm{k}_1$ and $\mathrm{k}_2$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is