JEE Main 2007 — Waves & Oscillations

A point mass oscillates along the $x$-axis according to the law $\mathrm{x=x_0 \cos (\omega t-\pi / 4)}$. If the acceleration of the particle is written as $\mathrm{a=A \cos (\omega t+\delta)}$

A sound absorber attenuates the sound level by $20 \mathrm{~dB}$. The intensity decreases by a factor of

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2 \times 10^{-2} \cos \pi t$ metres. The time at which the maximum speed first occurs is

Two springs, of force constants $k_1$ and $k_2$, are connected to a mass $\mathrm{m}$ as shown. The frequency of oscillation of the mass is $\mathrm{f}$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes 

A particle of mass $m$ executes simple harmonic motion with amplitude ' $a$ ' and frequency ' $v$ '. The average kinetic energy during its motion from the position of equilibrium to the end is