Question

The displacement of a particle executing SHM is given by y=0.25 sin 200t cm. Calculate the maximum speed of the particle.

Answer 1

see attachment...I hope it will helps....

Answer 2

Answer:

The maximum speed of the particle = 50 cm/s.

Explanation:

The displacement of the particle at an instant of time t, executing SHM is given by

$\rm y = 0.25\sin(200\ t)\ cm.$

The speed of the particle at any instant of time t is given by the rate of change of the position of the particle, i.e,

$\rm v(t)=\dfrac{dy}{dt}\\=\dfrac{d}{dt}\left ( 0.25\sin(200\ t)\ cm\right )\\=0.25\times 200\times \cos(200\ t)\ cm/s\\=50\cos(200\ t)\ cm/s.$

The speed of the particle is maximum when $\rm \cos(200\ t)$ will be maximum, the maximum value of $\rm \cos(200\ t)$ is 1.

Therefore, the maximum speed of the particle = $\rm v_{max}=50\times 1 = 50\ cm/s.$