Answer:
An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as
x(t) = x0 + A cos(ωt + φ).
The object oscillates about the equilibrium position x0. If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by
x(t) = A cos(ωt + φ).
A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction. Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The angular frequency ω is given by ω = 2π/T. The angular frequency is measured in radians per second. The inverse of the period is the frequency f = 1/T. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).
The velocity of the object as a function of time is given by
v(t) = dx(t)/dt = -ω A sin(ωt + φ),
and the acceleration is given by
a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.
