Show that the equation x- a sin `omegat` + b cos `omegat` represents a simple harmonic motion.

Show that the equation x=asinomegat+bcosomegat represents a simple harmonic motion.

Show that the equation x =acos^2omegat represents a simple harmonic motion. Find the:- amplitude.

Show that the equation x=acos^(2)omegat represents a simple harmonic motion. Find the (i) amplitude, (ii) time period and (iii) position of equilibrium of the particle.

Show that the equation x=Asinomegat represents a simple harmonic motion.

Show that the equation x=Acos(omegat-alpha) is a mathematical representation of simple harmonic motion. Find the time period and the maximum speed of the motion.

Show that the equation x=Asin(omegat-alpha) is the mathematical representation of a simple harmonic motion. Find the time period and the maximum acceleration of the motion.

y(t)=(sinomegat-cosomegat) represents simple harmonic motion, determine the period of SHM.

If the equation x=asinomegat represents a simple harmonic motion of a particle, then its initial position is

Write down the characteristics of simple harmonic motion.