Physics Course/Oscillation

Oscillation
Oscillation refers to any Periodic Motion moving at a distance about the equilibrium position and repeat itself over and over for a period of time. Example The Oscillation up and down of a Spring, The Oscillation side by side of a Spring. The Oscillation swinging side by side of a pendulum

Up and down Oscillation

 * Simple_harmonic_oscillator.gif

When apply a force on an object of mass attach to a spring. The spring will move a distance y above and below the equilibrium point and this movement keeps on repeating itself for a period of time. The movement up and down of spring for a period of time is called Oscillation

Any force acting on an object can be expressed in a differential equation
 * $$F = m \frac{d^2y}{dt^2}$$

Equilibrium is reached when
 * F = - Fy
 * $$F = m \frac{d^2y}{dt^2} = - k y$$
 * $$F = \frac{d^2y}{dt^2} + \frac{k}{m} y = 0$$
 * $$s^2 + \frac{k}{m} s = 0$$
 * $$s = \pm j \sqrt{\frac{k}{m}} t = \pm j \omega t = e^ j\omega t + e^ -j\omega t$$
 * $$y = A Sin \omega t$$

Side by Side Oscillation of Spring
When apply a force on an object of mass attach to a spring. The spring will move a distance x above and below the equilibrium point and this movement keeps on repeating itself for a period of time. The movement up and down of spring for a period of time is called Oscillation

Any force acting on an object can be expressed in a differential equation
 * $$F = m \frac{d^2x}{dt^2}$$

Equilibrium is reached when
 * F = - Fx
 * $$F = m \frac{d^2x}{dt^2} = - k x$$
 * $$F = \frac{d^2x}{dt^2} + \frac{k}{m} x = 0$$
 * $$s^2 + \frac{k}{m} s = 0$$
 * $$s = \pm j \sqrt{\frac{k}{m}} t = \pm j \omega t = e^ j\omega t + e^ -j\omega t$$
 * $$y = A Sin \omega t$$

Swinging Oscillation from side to side of Pendulum
When there is a force acting on a pendulum. The pendulum will swing from side to side for a certain period of time. This type of movement is called oscillation


 * Simple_pendulum_height.svg
 * $$m g = -l y$$
 * $$y = \frac{m g}{l}= v t$$
 * $$t =\frac{m g}{l v}$$ ||

Summary

 * 1) Oscillation is a periodic motion.
 * 2) Oscillation can be thought as a Sinusoidal Wave.
 * 3) Oscillation can be expressed by a mathematic 2nd order differential equation
 * {| class="wikitable" width=100% align=center

! Oscillation !! Picture !! Force !! Acceleration !! Distance travel !! Time Travelled
 * /Spring Oscillation/
 * When there is a force acting on a spring . The spring goes into an up and down motion for a certain period of time . This type of movement is called oscillation
 * When there is a force acting on a spring . The spring goes into an up and down motion for a certain period of time . This type of movement is called oscillation


 * $$m a = -ky$$

$$m \frac{d^2y}{dt^2} = -ky$$ $$m \frac{d^2y}{dt^2} + ky = 0 $$ $$s = \pm j \sqrt{\frac{k}{m}}$$ $$y = e^{j\sqrt{\frac{k}{m}}t} + e^{-j\sqrt{\frac{k}{m}}t}$$ $$y = y_m \cos \left(\sqrt{\frac{k}{m}}t\right)$$
 * $$a = \frac{k}{m}y $$
 * $$y = \frac{ma}{k}= a t^2 $$
 * $$t = \pm\sqrt{\frac{k}{m}}$$
 * /Pendulum Oscillation/
 * When there is a force acting on a pendulum. The pendulum will swing from side to side for a certain period of time . This type of movement is called oscillation.
 * When there is a force acting on a pendulum. The pendulum will swing from side to side for a certain period of time . This type of movement is called oscillation.


 * $$m g = -l y$$
 * $$y = \frac{m g}{l}= v t$$
 * $$t =\frac{m g}{l v}$$
 * }
 * }
 * }