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Simple Harmonic Motion (SHM), WAVE- An oscillation that transfers energy…

- - - - The negative sign shows that the direction of the force is always opposite to the displacement. By Newton's Second Law, F=ma, therefore ma= -kx.
- - - - At equilibrium, the force of the spring equals the weight of the load. Hence, the force equation is given as : mg - ke =0, where k is the spring constant.
      - If a is the acceleration of the load at a position x below the equilibrium position, the net force becomes : a= -kx/m or a= -w^2x
        
        The systems performs a SHM with angular frequency :
- - - - A particular example is the SHM of a spring with a frictional force that is directly proportional to its velocity. In the presence of damping force, the resultant force on the body is, The sum of F= -kx-bv
        
        When the damping is so large that b becomes infinity, and w'=0
        
        When the condition in the above equation is satisfied, thus the system is under critical damping.
  - - - This additional force is called the driving force and the motion is forced oscillation.
  - - - Example : When a lorry passes by at a certain speed, the road seems to vibrate because of the resonance. In this case, the frequency of the lorry equals the natural frequency of the road.
- - - - Fundamental frequency : The lowest frequency of vibration that produces a stationary waves with one antinode
        
        Referred as first harmonics, first overtone as second harmonic, second overtone as third harmonic and so on.
      - Other resonance frequencies called overtones and are found to be multiples of fundamental frequency.
  - - - The antinodes correspond to the close end of the tube because at that position the air is not free to move and the air displacement is minimum. A t the open end, where air molecules are free to move it corresponds to the antinodes.