Energy of simple harmonic motion

1. Body on a spring.

When an object is attached to a spring and undergo simple harmonic motion, the force on the spring is given by ;

The work done in stretching the spring is given by

Work = Average force  x  displacement

This work is converted to energy , hence the energy stored in the stretched spring=

This potential energy is converted to kinetic energy when the string is released. The kinetic energy is given by   where m is the mass of the body and v is the velocity at that instant.

The total energy at any point is constant and is equal to the sum of the potential and kinetic energy.

P.E +K.E= constant

At the equilibrium position where the speed is maximum, P.E=0, since x=0 .

At this point , total energy =   =  

At maximum position where the speed v=0

At any other position , as K.E increases , P.E decreases and as P.E increases K.E decreases.  Total energy at any point = P.E + K.E

2. Simple pendulum

The conservation of energy  is also applicable to simple pendulum as shown in the diagram

TOTAL ENERGY AT ANY POINT = P.E + K.E= CONSTANT

From the diagram above ,as the pendulum go from center c to A . K.E decreases and P.E increases . note that at any point total energy remain the same this is equal

P.E + K.E= constant

  ,for simple pendulum

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