Explanation:
This is a simple harmonic motion, produced by the action of a driving force that is directly proportional to the position of the body. Its position is described as a function of time by a sinusoidal function. According to Newton's second law and Hooke's law:
[tex]F=m\frac{d^2x}{dt^2}\\F=-kx[/tex]
Here m is the object's mass, k is the spring constant and x is the displacement from the equilibrium position.
[tex]m\frac{d^2x}{dt^2}=-kx\\\frac{d^2x}{dt^2}=-\omega_0^2x\\x=Asin(\omega_0 t-\phi)[/tex]
With [tex]\omega_0=\sqrt{\frac{k}{m}}[/tex], called natural frequency, A is the amplitude, that is the maximum displacement for the equilibrium position and [tex]\phi[/tex] is the initial phase.
