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. I) sinomegat-cosomegat 2) sin^(2)omegat

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. I) sinomegat-cosomegat 2) sin^(2)omegat
Answer» Solution :`sinomegat-COSOMEGAT= sqrt(2)[(1)/(sqrt(2))sinomegat-(1)/(sqrt(2))cosomegat]= sqrt(2)[sinomegatcos((pi)/(4))-cosomegatsin((pi)/(4))]= sqrt(2)sin(omegat-pi//4)` This function REPRESENTS a simple HARMONIC motion having a period `T= (2pi)/(omega)` and a PHASE angle `(pi//4)` or `(7pi//4)` 2) `sin^(2)omegat= (1-cos2omegat)/(2)= (1)/(2)-(1)/(2)cos2omegat` The function is periodic having a period `T = T//omega`. It also represents a harmonic motion with the point of EQUILIBRIUM occurring at `1//2` instead of zero.