The figure shows the displacement-time graph of a particle executing `SHM`. If the time period of oscillation is `2s`, then the equation of motion is given by

Options

A. `x = 10sin (pit + pi//3)`
B. `x = 10 sinpit`
C. `x = 10sin(pit+pi//6)`
D. `x =10 sin(2pit + pi//6)`

Answer

C

Explanation

From figure
maximum amplmitude ltbRgt Position of particle at `t = 0`,
let equation of SHM is
`x = Asin(omegat + phi)` At `t = 0, x = 5` ltbRgt `5 = 10 sinphi rArr phi = pi//6` and `omega = (2pi)/(T) = (2pi)/(2) = pi`
Thus, equation of SHM `x = 10 sin(pit + (pi)/(6))`.