Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic motion? Give the period for each case. (i) sinomegat-cosomegat (ii) sin^(2)omegat (iii) cosomegat+2sin^(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 motion? Give the period for each case. (i) sinomegat-cosomegat (ii) sin^(2)omegat (iii) cosomegat+2sin^(2)omegat
Answer» a simple HARMONIC MOTION with a period `(pi)/(omega)`. a simple harmonic motion with a period `(2pi)/(omega)` a PERIODIC, but not simple harmonic motionn with a period `(pi)/(omega)` a periodic, but not simple harmonic motion with a period `(2pi)/(omega)` Solution :`sinomegat-cosomegat=sqrt(2)((1)/(sqrt(2))sinomegat-(1)/(sqrt(2))cosomegat)` `=sqrt(2)(sinomegat"cos"(pi)/(4)-cosomegat"sin"(pi)/(4))=sqrt(2)sin(omegat-(pi)/(4))` It represented SHM with a period `(2pi)/(omega)`.