Features of Motion

The frequency
A simple oscillating system consists of a particle moving repeatedly back and forth about a reference origin. an important property of this kind of systems is its frequency, which is the number of completed oscillations ( or cycles) per second. We usually use the symbol f and the unit of the frequency is called the Hertz (abbreviated Hz).

The period
Another important property of an oscillatory motion is its period T, which is the time for one complete cycle (or oscillation). the period is related to the frequency via the formula

T=1/f

Obviously, the unit for the period is the second s.

The amplitude
The amplitude of a sinusoidal motion, like the one described in the previous formula, is given by x_m. The subscript m stands for maximum because the amplitude is the magnitude of the maximum displacement of the particle in either direction about the origin. Since the cosine function oscillates between -1 and +1, then the displacement x(t) varies between -x_m and +x_m.

The phase
The equation of the displacement contains the term (Alpha*t+Phy) which is called the phase of the motion, and the constant Phy is called the phase constant (or phase angle).The value of the phase constant depends on the displacement and the velocity of the particle at the time t=0, and its SI unit is the radian.

The acceleration
We know that the acceleration of a particle is simply the derivative, with respect to time, of the velocity of that particle. Knowing the velocity v(t) for simple harmonic motion, we can calculate the acceleratioa.