A 100 g block is connected to a horizontal massless spring of force constant `25.6(N)/(m)` As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at `t=0`, it is released from rest at `x=0` It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time `(x-t)` graph of motion of the block is as shown in Fig.
Velocity of the block as a function of time can be expressed as

Options

A. `v=-sin48(16t(pi)/(2))(cm)/(s)`
B. `v=-48sin(16t(pi)/(3))(cm)/(s)`
C. `v=-56sin(16t(pi)/(4))(cm)/(s)`
D. `v=-56(16t(pi)/(6))(cm)/(s)`

Answer

D

Explanation

Differentiating previous result
`v=-31sqrt3sin(16t+(pi)/(6))(cm)/(s)`