Which of the following functions of time represent (a) simple harmonic motion and b. periodic but not simple harmonic? Give the period for each case. (1) sin omega t -cos omega t 2. sin^(2)omega t

Which of the following functions of time represent (a) simple harmonic

1.	Which of the following functions of time represent (a) simple harmonic motion and b. periodic but not simple harmonic? Give the period for each case. (1) sin omega t -cos omega t 2. sin^(2)omega t
Answer» Solution :1. `SIN omega t -cos omega t =SQRT(2)[1/(sqrt(2)) sin omega t-1/(sqrt(2))cos omegat]` `=sqrt(2)[sin omega t "cos"(pi)/4-cos omega t "sin"(pi)/4]` `=sqrt(2)sin(omega t-pi//4)` This FUNCTION represents a simple harmonic motion having a period `T=(2pi)/(omega)` and a phae angle `(-pi//4)` or `(7pi//4)` 2. `sin^(2)omegat=(1-cos2omegat)/2=1/2-1/2cos 2omegat` The function is periodic having a period `T=pi//3omega`. It also represents a haromonic motion with the point ofequilibrium OCCURRING at 1/2 instead of zero.