JEE Main 2013 — Physics Waves & Oscillations

Match List-I with List-II. <table class="pyq-table"><tbody><tr><th>List-I</th><th>List-II</th></tr><tr><td>A. $\sin^2 \omega t$</td><td>I. Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)</td></tr><tr><td>B. $\sin^3(2\omega t)$</td><td>II. Periodic with time period $T = \dfrac{2\pi}{\omega}$ but Not SHM</td></tr><tr><td>C. $\sin(\omega t) + \cos(\pi \omega t)$</td><td>III. Periodic with time period $T = \dfrac{\pi}{\omega}$ and SHM</td></tr><tr><td>D. $\cos\omega t + \cos 2\omega t$</td><td>IV. Non-periodic</td></tr></tbody></table> Choose the correct answer from the options given below :

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in the figure. For small oscillations the time period is ______. ($g$ is acceleration due to gravity) 

The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2 = 50 - x^2$, where $x$ represents displacement. If the time period of motion is $\dfrac{x}{7}$ s, the value of $x$ is _____.

A spring stretches by $2$ mm when it is loaded with a mass of $200$ g. From equilibrium position the mass is further pulled down by $2$ mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g $= 10$ m/s$^2$)

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is : $k=150 \mathrm{~N} / \mathrm{m}$