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Wize High School Grade 12 Physics Textbook > Oscillations

Basic Concepts of Oscillation

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Simple Harmonic Motion



Simple Harmonic Motion (SHM) is a type of periodic motion in which:
  • The restoring force is proportional to the displacement from the equilibrium position
  • The Force direction is opposite to that of displacement.

F=−kx\boxed{F=-kx}


Wize Tip
Any physical system with the above type of the force undergoes a Simple Harmonic Motion. Constant kk in the above equations depends on the physical property of the oscillating system.


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The mathematical description of SHM is a sinusoidal function of time:


  x(t)=Acos⁡(ωt)  \boxed{\ \ x\left(t\right)=A\cos\left(\omega t\right)\ \ }




Watch Out!
SHM can be described by either sine or cosine function!

These are the parameters we use to describe a simple harmonic motion:

  • Amplitude (A): The maximum displacement of the object from the equilibrium.
  • Period (T): The time it takes for one complete oscillation (Period is measured in seconds).

T=Total timenumber of cycles\boxed{T=\frac{Total\ time}{number\ of\ cycles}}

  • Frequency (f): The number of oscillations per unit of time (Frequency is measured in Hertz (1 Hz=1/s)).
f=1T\boxed{f=\dfrac{1}{T}}

  • Angular frequency (ω\colorFour{\omega}): The rate at which argument of sinusoidal function describing oscillation changes in time (Angular frequency is measured in rad/srad/s).

ω=2πf=2πT\boxed{\omega=2\pi f=\dfrac{2\pi}{T}}

Write the equation of motion for a 2.3 kg mass attached to a spring with constant 8.0 N/m, when the mass is released from rest at 0.15 m from equilibrium.

x(t) = A cos (wt)

A = 0.15 m
m = 2.3 kg
k = 8.0 N/m

w = sqrt (k/m) = sqrt (8.0/2.3) = 1.9 rad/s

x(t) = 0.15 cos (1.9t)