When a particle executing S H M is $2 \mathrm{cm}$ Away from the mean position its kinetic energy is double the potential energy. At what distance from the mean position will the P.E. be double the K.E.?

A particle is subjected to two simple harmonic motions in the same direction having equal amplitude and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions, find the phase difference between the individual motions.

The displacement of a simple harmonically vibrating particle when observation starts is given by $x=5 \sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetre and $t$ in second. When does the particle first comes to rest?

The displacement of a simple harmonically vibrating particle when observation starts is given by $x=5 \sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetre and $t$ in second. When does the particle first have zero acceleration?

The displacement of a simple harmonically vibrating particle when observation starts is given by $x=5 \sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetre and $t$ in second. When does the particle first have maximum speed?

A particle is subjected to two simple harmonic motions of the same time period in the same direction. The amplitudes of the first motion is $3.0 \mathrm{cm}$ and that of the second $4.0 \mathrm{cm}$. Find the resultant amplitude if the phase difference between the motions is $0°$.

A particle is subjected to two simple harmonic motions of the same time period in the same direction. The amplitudes of the first motion is $3.0 \mathrm{cm}$ and that of the second $4.0 \mathrm{cm}$. Find the resultant amplitude if the phase difference between the motions is $30°$.

A particle is subjected to two simple harmonic motions of the same time period in the same direction. The amplitudes of the first motion is $3.0 \mathrm{cm}$ and that of the second $4.0 \mathrm{cm}$. Find the resultant amplitude if the phase difference between the motions is $60°$.