Simple Harmonic Motion

Simple Harmonic Motion

1. oscillating motion

   • acceleration id directly proportional to the displacement
   • Acceleration is in the opposite direction to the displacement
   • a= -(2pif)^2 X
   • x= Acos(2pift)
   • V= 2pif sqroot[A^2-x^2]
   • max speed= 2pifA
   • Max acceleration (2pif)^2 A

2. shm systems

   • Simple Pendulum
     • T= 2pi Sqroot[l/g}]
     • length influences time period
   • Mass-spring system
     • T= 2pi Sqroot[m/k]
     • T is relative to spring constant and mass

3. Variation of energy with time

   • beware energy is not negative
   • Really good link for energy change with time on mass spring system
     • http://zonalandeducation.com/mstm/physics/mechanics/energy/massOnASpring/massOnASpring.html

4. Forced vibrations and resonance

   • natural frequency= when a system oscillates without a periodic force
   • when a periodic force is applied a system it undergoes forced oscillations
   • resonance
     • applied frequency is equal to the natural frequency
     • amplitude of oscillations become very large and violent
     • examples include car suspension and bridges
     • resonance 90 degree (pi/2) difference between driving force and driven oscillations
   • Damping
     • forces that cause damping are called dissipative forces
     • Light Damping
       • displacement and amplitude gradually decrease with each time period
     • Critical Damping
       • just enough to stop the system oscillating after it has been displaced
     • Heavy Damping
       • damping so strong that displaced object returns to equilibrium more slowly than if it's critically damped

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