Key Concepts: Energy in SHM

Energy in Simple Harmonic Motion

• In SHM, energy continuously converts between kinetic energy and potential energy.
• Total mechanical energy: E = ½kA² (constant, if no damping).

At Key Positions

• Equilibrium (x = 0): PE = 0, KE = maximum = ½kA². Speed is maximum.
• Extremes (x = ±A): KE = 0, PE = maximum = ½kA². Speed is zero.
• At any position: KE + PE = ½kA² → ½mv² + ½kx² = ½kA².

Graphs

• KE and PE are both sinusoidal and oscillate at twice the frequency of the motion.
• When KE is at its peak, PE is at its minimum, and vice versa.
• Total energy is a horizontal line on an Energy vs. Time graph.