🌀 Elasticity & Harmonic Oscillators
Hooke's Law & Spring Constant Calculator
Compute spring restoring force ($F = kx$), stored elastic potential energy ($U = \frac{1}{2}kx^2$), spring stiffness ($k$), and mass-spring harmonic oscillation frequencies.
Elastic Parameters
N/m
kg
Restoring Force (F)
50.00 N
Stored Energy ($U$)
5.00 J
Natural Period ($T$)
0.562 s
Frequency ($f$)
1.78 Hz
💡 Spring Combination Equivalents:
Two identical springs in Parallel: $k_{\text{eq}} = 500\text{ N/m}$ • In Series: $k_{\text{eq}} = 125\text{ N/m}$.
Hooke's Law & Simple Harmonic Oscillations
Robert Hooke discovered that elastic deformation is proportional to applied load:
- Restoring Force: $$F = -k x$$
- Elastic Potential Energy: $$U = \int_0^x k s \, ds = \frac{1}{2} k x^2$$
- Harmonic Oscillation Period: $$T = 2\pi\sqrt{\frac{m}{k}}, \quad f = \frac{1}{T} = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$