Question

A particle start form mean position and moves towards positive extreme as shown. Find the equation of the `SHM`. Amplitude of `SHM` is `A`.

Answer 1

General equation of `SHM` can be written as `x = A sin (omegat + phi)`
At `t = 0, x = 0`
`:. 0 = A sinphi`
`:. Phi = 0, pi, phi in [0,2pi)`
Also, at `t = 0, v = +ve`
`:. A omega cosphi = +ve`
or, `phi = 0`
Hence, if the particle is at mean position at `t = 0` and is moving towards `+ve ` extreme, then the equation of `SHM` is given by `x = A sinomegat`
Similarly
for `phi = pi`
`:.` equation of `SHM` is `x = A(omegat + pi)`
or, `x = -A sinomegat`