Question

A particle starts from mean position and moves towards positive extreme as show below. Find the equation of the `SHM`, Amplitude of `SHM` is `A`.

Answer 1

General equation of `SHM` can be written as `x = Asin(omegat+phi)`
At `t = 0, x = 0 , :. 0 = Asinphi, :. phi = 0, pi , phiin[0,2pi]`
Also, at `t = 0, v = +ve , :. Aomegacosphi = "maximum" +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 = Asinomegat`

Similarly, for particle moving towards `-ve` extreme then `phi = pi`
`:.` equation of `SHM` is `x = Asin(omegat + pi)` or, `x = -Asinomegat`