3. Energy in Simple Harmonic Motion

What are the Changes in Energy during S.H.M.?

Continual change of kinetic energy to potential energy and vice-versa.

What is constant in an ideal S.H.M. system?

Total energy (E_T) remains constant with time (no dissipative forces).

What is Total Energy (E_T) in S.H.M.?

ET = EK + E_P.

What is Kinetic Energy (E_K) at displacement x from equilibrium?

E_K = ½mv² = ½mω²(x₀² - x²).

What is Potential Energy (E_P) at displacement x from equilibrium?

EP = ½kx² = ½mω²x². (Assuming EP = 0 at equilibrium).

When is Kinetic Energy maximum in S.H.M.?

At x = 0 (equilibrium position) -> E_K,max = ½mω²x₀².

When is Potential Energy maximum in S.H.M.?

At x = ±x₀ (amplitude positions) -> E_P,max = ½mω²x₀².

What is the total energy in S.H.M.?

E_T = ½mω²x₀². It is constant and does not depend on displacement x.