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

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

A whistle producing sound waves of frequencies $$9500$$ $$Hz$$ and above is approaching a stationary person with speed $$v$$ $$m{s^{ - 1}}.$$ The velocity of sound in air is $$300\,m{s^{ - 1}}.$$ If the person can hear frequencies upto a maximum of $$10,000$$ $$HZ,$$ the maximum value of $$v$$ upto which he can hear whistle is

A string is stretched between fixed points separated by $$75.0$$ $$cm.$$ It is observed to have resonant frequencies of $$420$$ $$Hz$$ and $$315$$ $$Hz$$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is