JEE Main 2006 — Waves & Oscillations

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7 \mathrm{~mm}$, is $4.4 \mathrm{~m} / \mathrm{s}$. The period of oscillation is

Starting from the origin, a body oscillates simple harmonically with a period of $2 \mathrm{~s}$. After what time will its kinetic energy be $75 \%$ of the total energy?

A string is stretched between fixed points separated by $75 \mathrm{~cm}$. It is observed to have resonant frequencies of $420 \mathrm{~Hz}$ and $315 \mathrm{~Hz}$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time