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Waves
Waves

SHM Total Energy

E=12kA2=12mω2A2E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2

Total mechanical energy in SHM is constant.

Variables

E
Total energy
Constant total energy
J
k
Spring constant
Spring stiffness
N/m
A
Amplitude
Maximum displacement
m
m
Mass
Oscillating mass
kg
ω
Angular frequency
ω = √(k/m)
rad/s

Derivation

E = KE + PE = ½mv² + ½kx² = ½kA² (at max displacement).

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Common questions

What is the SHM Total Energy formula?

SHM Total Energy is written E = 1/2kA² = 1/2mω² A². Total mechanical energy in SHM is constant. It belongs to Waves, under Simple Harmonic Motion.

What are the units in E = 1/2kA² = 1/2mω² A²?

In SI units, E is total energy, measured in kg·m²/s²; k is spring constant, measured in kg/s²; A is amplitude, measured in m; m is mass, measured in kg; ω is angular frequency, measured in rad/s.

How is the SHM Total Energy formula derived?

E = KE + PE = ½mv² + ½kx² = ½kA² (at max displacement). The result is E = 1/2kA² = 1/2mω² A².