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Spring-Mass Shm Oscillator

Resonance

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Damping proportional to velocity

1. Three cases:
   • Lightly damped SHM:
     There is an oscillation but the amplitude decreases exponentially with time.
   • Heavily damped SHM:
     There is no real oscillation. There is only a very slow return of the object to the initial equilibrium position.
   • Critically damped SHM:
     There is no real oscillation. It returns to the equilibrium position in the shortest time.
     
     
2. The period of a lightly damped SHM is slightly longer than that of the undamped.
   
   
3. Test for exponential decay: A_o/A₁ = A₁/A₂ = A₂/A₃ = .....
   
   
   
   

Damping due to Solid Friction

1. The amplitude decreases linearly with time. Therefore, A_o - A₁ = A₁ - A₂ = A₂ - A₃ = .....
   
   
   
   
   
2. The oscillator may finally stop at a point with a nonzero displacement.