In example 34, let us take the position of the mass, when the spring is unstretched, as x=0, and the direction from left to right as the positive direction of X-axis. Give x as a function of time t for the oscillating mass, if at the moment we start the stop watch (t=0), the mass is (i) at the mean position (ii) at the maximum stretched position (iii) at the maximum compressed position.
In what do these different functions of SHM differ ? Frequency, amplitude or initial phase ?

Explanation

Here, `a=2.0cm, omega=sqrt((k)/(m))=sqrt((1200)/(3))=20s^(-1)`
(a) As time is noted from the mean position, hence using `x=asinomegat`, we have `x=2sin20t`
(b) At maximum stretched position, the body is at the extreme right position, with and intial phase of `pi//2` rad. Then, `x=1sin(omegat+(pi)/(2))=acosomegat=2cos20t`
(c) At maximum compressed position, the body is at the extreme left position, with an intial phase of `3ph//2` rad. Then, `x=asin(omegat+(3pi)/(2))=-acosomegat=-2cos20t`
The functions neither differ in amplitude nor in frequency. They differ in initial phase.