Chapter 13  Vibrations and Waves

1.  Hook's law:    Restoring force of a spring          F =  -k x

2. Simple Harmonic Motion (SHM)-  occurs whenever the restoring force on the system is proportional to the displacement and opposed to it.

                                     F = - kx

                                     x =  A cos wt;   v = -Aw sin wt

                                      w = 2p /T;      w = Ö( k/m)

                                    PE_elastic =  ½ kx²

   Simple pendulum-   A point mass attached to a light string

                                    T = 2pÖ (L/g)  

  Damped harmonic motion:  motion with a retarding force- oscillations die out, 

   Driven harmonic oscillator:  The oscillator is driven by an outside periodic force

   Resonance- occurs when the oscillator is driven at its natural frequency

 3. Wave  Motion

     Waves-     a traveling disturbance

                       carry energy

                      speed determined by the properties of the traveling medium

     Wave types-  Transverse waves

                           Longitudinal waves

      Wavelength (l), frequency (f), wave velocity (v)   ;    v = lf

      Speed of a wave on a string-  depends on the tension in the string and the mass per unit length of the string (inertia)

4.   Interference of waves

     Reflection of waves

     Sound waves