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 $60°$.

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 $90°$.

Find the amplitude of the resultant motion. Three simple harmonic motions of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is ${60}^{\circ }$ ahead of the first and the phase of the third motion is ${60}^{\circ }$ ahead of the second.

Two simple harmonic motions, each of amplitude $10 \mathrm{cm}$ and frequency $5 \mathrm{Hz}$, along two perpendicular directions superpose on each other. Show that the resultant motion would be along a circle if the phase difference between them is $\frac{\mathrm{\pi }}{2}$. Find the radius of the circle and time period of the circular motion.

A source having a frequency of $50Hz$ Produces cosine waves of wavelength $2 m$ and the maximum amplitude of vibration in that wave is $10 cm$. Represent the equation of wave generated by this source, if this wave moves along $\left(-Y\right)-axis$ and the vibration of particles are along $X-axis$.