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) 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. (1) sinomegat-cosomegat (2) sin^(2)omegat
Answer» <html><body><p></p>Solution :(a) `sinomegat-cosomegat` <br/> `=sinomegat-sin(pi//<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>-omegat)` <br/> `=2cos(pi//4)sin(omegat-pi//4)` <br/> `=sqrt2sin(omegat-pi//4)` <br/> This function represents a simple harmonic motion having a period `T=2pi//omega` and a <a href="https://interviewquestions.tuteehub.com/tag/phase-22748" style="font-weight:bold;" target="_blank" title="Click to know more about PHASE">PHASE</a> angle `(-pi//4)` or `(7pi//4)` <br/> (b) `sin^(2)omegat` <br/> `=1//2-1//2cos2omegat` <br/> The function is periodic having a period `T = pi//omega`. It also represents a harmonic motion with the point of equilibrium <a href="https://interviewquestions.tuteehub.com/tag/occurring-1127842" style="font-weight:bold;" target="_blank" title="Click to know more about OCCURRING">OCCURRING</a> at `1//2` <a href="https://interviewquestions.tuteehub.com/tag/instead-516622" style="font-weight:bold;" target="_blank" title="Click to know more about INSTEAD">INSTEAD</a> of zero.</body></html>