2.3 Restoring Force and Energy in Simple Harmonic Motion

2.3 Restoring Force and Energy in Simple Harmonic Motion

Restoring Force:

The restoring force in SHM is the force that brings the object back to its equilibrium position. It is proportional to the displacement and acts in the opposite direction.

Kinetic and Potential Energy:

- **Kinetic Energy (K.E.):** The kinetic energy of an object in SHM at a displacement x is given by:

K.E. = 1/2 mω²(A² - x²)

- **Potential Energy (P.E.):** The potential energy stored in the system at displacement x is given by:

P.E. = 1/2 kx²

- **Total Mechanical Energy:** The total energy in SHM is constant and is the sum of kinetic and potential energy:

E = 1/2 kA²

Example Problem:

A block of mass 2 kg is attached to a spring with a spring constant of 100 N/m. If the block is displaced 0.2 m from the equilibrium position, find the total mechanical energy of the system.

Solution:

The total mechanical energy is given by:

E = 1/2 kA² = 2 J