Simple Harmonic Motion

Simple Harmonic Motion

1. e.g. pendulum that is moving with SHM

2. REMEMBER: AMPLITUDE=MAXIMUM DISPLACEMENT

   • ∆velocity = gradient of displacement time graph
   • velocity is greatest when amplitude = zero
   • amplitude is greatest (maximum displacement) when velocity=0
   • Acceleration is greatest when velocity=0 ∴ maximum displacement also.
   • ACCELERATION IS ALWAYS IN THE OPPOSITE DIRECTION TO THE DISPLACEMENT
     • A= -k x displacement

3. ·

   • a = v²/r
     • v = 2πrf
       • a=(2πrf )²/r
         • a=(2πf)²r
           • for SHM
             • a=-(2πf)²r
               • r= displacement

4. x = r cosΘ

5. y = r sin Θ

6. ALWAYS CALCULATE IN RADIANS

7. Resonance

   • Resonance is the tendency of a system to oscillate with a larger amplitude at some frequencies than at others.
   • * Between the displacement and applied periodic force
   • At resonance, applied frequency of a periodic force= nTURAL FREQUENCY OF THYE SYSTEM

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