In question. Let us take position of 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 it at the moment we start the stoop watch (t=0) , the mass is (a) at the mean position (b) at the maximum streteched position, and (c) at the maximum compressed position. In what way do these functions for S.H.M. differ from each other, in frequency, in amplitude or initial phase ?

In question. Let us take position of mass when the spring is unstretch

1.	In question. Let us take position of 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 it at the moment we start the stoop watch (t=0) , the mass is (a) at the mean position (b) at the maximum streteched position, and (c) at the maximum compressed position. In what way do these functions for S.H.M. differ from each other, in frequency, in amplitude or initial phase ?
Answer» Solution :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.