Does damped simple harmonic motion strictly simple harmonic?

Define simple harmonic motion.

Why is the simple harmonic motion so named?

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 (co is any positive constant): sin^3omegat

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 (co is any positive constant):3 cos ((pi/4)-(2omegat))

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 (co is any positive constant): sin omegat -cos omegat

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 (co is any positive constant): cos omegat+cos3omegat=cos 5omegat