Why periodic time `T= (2pi)/(omega)` of function `f(t)= A cos omega t` should be taken?

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ( omega is any positive constant): (a) sinomegat-cosomegat (b) sin^(3)omegat (c) 3cos(pi//4-2omegat) (d) cosomegat+cos3omegat+cos5omegat (e) exp(-omega^(2)t^(2)) (f) 1+omegat+omega^(2)t^(2)

Find the resulting amplitude A' and the phase of the vibrations delta S = Acos(omegat) + A/2 cos (omegat + pi/2) + A/2 cos (omega t + pi) + A/8 cos (omegat + (3pi)/(2)) = A' cos (omega t + delta)

A particle is acted simultaneouosly be mutually perpendicular simple harmonic motion x= a cos omega t" and "y= a sin omega t . The trajectory of motion of the particle will be………

When two waves y _(1) =A sin (omega t + (pi)/(6)) and y _(2) = A cos (omega t) superpose, find amplitude of resultant wave.

Path different between waves y_(1) = A_(1) sin (omega t - (2pix)/(lamda)) and y _(2) = A_(2) cos (omega t - (2pi x)/(lamda) + phi) at the point of superpositon is :

When two displacements represented by y_(1)= a sin(omega t)" and "y_(2)= b cos (omega t) are superimposed the motion is…….