Relation between Potential Energy and Kinetic Energy in SHM
Potential energy and kinetic energy in simple harmonic motion (SHM) are interrelated through the principle of conservation of mechanical energy.

Potential Energy in SHM
- In SHM, potential energy is stored in the system when the object is displaced from its equilibrium position.
- The potential energy of an object undergoing SHM can be expressed as:
\(PE = \frac{1}{2}kx^2\)
where \(k\) is the spring constant and \(x\) is the displacement from the equilibrium position.

Kinetic Energy in SHM
- Kinetic energy in SHM arises from the motion of the object as it oscillates back and forth.
- The kinetic energy of an object undergoing SHM can be defined as:
\(KE = \frac{1}{2}mv^2\)
where \(m\) is the mass of the object and \(v\) is the velocity.

Relation between Potential and Kinetic Energy
- At any point in the motion of the object, the total mechanical energy (sum of potential and kinetic energy) remains constant.
- Therefore, in SHM, the total mechanical energy can be expressed as:
\(E = PE + KE = \frac{1}{2}kx^2 + \frac{1}{2}mv^2\)
- This equation illustrates the relationship between potential and kinetic energy in SHM, showing that as potential energy increases, kinetic energy decreases, and vice versa.
- The total mechanical energy of the system remains constant throughout the oscillation, demonstrating the conservation of energy in SHM.