Last modified on 19 July 2012, at 20:27

Physics Course/Oscillation

OscillationEdit

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

Spring's OscillationEdit

Up and down OscillationEdit

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 SpringEdit

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 site to site of PendulumEdit

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} ||

SummaryEdit

  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
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

Simple harmonic oscillator.gif

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
Simple pendulum height.svg
m g = -l y y = \frac{m g}{l}= v t t =\frac{m g}{l v}