Write the equation of SHM for the situations show below:

Explanation

(a) At `t = 0, x = +A`
`x = Asin(omegat + phi)`
`A = Asin(phi)`
`phi = pi//2`
`x = A sin (omegat + (pi)/(2)) = Acos(omegat)`
(b) At `t = 0, x = -A`
`x = A sin(omegat + phi)`
`-A = Asin phi`
`phi = (3pi)/(2)`
`x = A sin(omegat + (3pi)/(2))`
`x = -A cos (omegat)`
(c) At `t = 0, x = (A)/(2)`
`x = A sin (omegat + phi)`
`(A)/(2) = A sin (omegat + phi)`
`(1)/(2) = sin phi rArr phi = 30^(@), 150`
Particle is moving towards the mean position and in negative direction.
velocity `v = Aomega cos (omegat + phi)`
At `t = 0, v = -ve`
hence `v = Aomegacis phi`
hence `phi = 150^(@)`
`x = A sin(omegat + 150^(@))`
(a) `x = Acosoemgat`, (b) `x = -A cosomegat`, (c) `x = Asin(omegat + 150^(@))`