\[U=\frac{1}{2}kx^2\]
Variables
Upotential energy (J)
kspring constant (N/m)
xdisplacement from equilibrium (m)
Description
What is this formula?
The harmonic oscillator potential energy formula calculates the elastic potential energy stored in a system undergoing harmonic motion.
When to use it
Use this formula in classical mechanics, molecular physics, vibration analysis, and quantum mechanics when modeling springs or harmonic restoring forces.
Example
A spring has:
k = 250 N/m
x = 0.08 m
Formula:
U = (1/2)*k*x²
Substitution:
U = (1/2) × 250 × (0.08)²
Result:
U = 0.80 J
The harmonic oscillator stores 0.80 J of potential energy.
Applications
- Spring mechanics
- Vibrational systems
- Molecular bond approximations
- Oscillation analysis
- Quantum harmonic oscillator models