Hooke's Law Calculator
Spring force, elastic potential energy, and oscillation period.
Inputs
Results
Restoring Force (N)
5
Elastic PE (J)
0.13
Oscillation Period (s)0.63
Frequency (Hz)1.59
Angular Frequency (rad/s)10
Max Velocity (m/s)0.5
Max Acceleration (m/s²)5
How to Use This Calculator
- Enter spring constant k (N/m) — higher values mean a stiffer spring.
- Enter displacement x (m) from the equilibrium position — positive for stretch, negative for compression.
- Enter attached mass (kg) for oscillation calculations.
- Read restoring force (N) and elastic potential energy (J) stored in the spring.
- Review oscillation period (s), frequency (Hz), and maximum velocity (m/s) for the spring-mass system.
How the result changes with Spring Constant k (N/m)
| Spring Constant k (N/m) | Restoring Force (N) | Elastic PE (J) |
|---|---|---|
| 10,000,000 | 500,000 | 12,500 |
| 35,000,000 | 1,750,000 | 43,750 |
| 65,000,000 | 3,250,000 | 81,250 |
| 90,000,000 | 4,500,000 | 112,500 |
What each input means
- Spring Constant k (N/m)
- Stiffness of the spring in newtons per meter.
- Displacement x (m)
- Distance stretched or compressed from equilibrium.
- Attached Mass (kg)
- Mass attached to the spring (for oscillation calculations).
What each result means
- Restoring Force (N)
- F = kx. Force magnitude pulling back to equilibrium.
- Elastic PE (J)
- PE = ½kx². Energy stored in the spring.
- Oscillation Period (s)
- T = 2π√(m/k). Time for one complete oscillation.
- Frequency (Hz)
- f = 1/T. Oscillations per second.
- Angular Frequency (rad/s)
- ω = 2πf.
- Max Velocity (m/s)
- v_max = ωA at equilibrium (if x is amplitude).
- Max Acceleration (m/s²)
- a_max = ω²A at maximum displacement.
How this is calculated
Worked example, using the default values
- Identify Input ParametersSpring Constant k (N/m) = 100, Displacement x (m) = 0.05, Attached Mass (kg) = 1 = 3 input(s) provided
- Calculate Restoring ForceRestoring Force = springConstant * absDisp5 = 5
- Calculate Elastic PEElastic PE = 0.5 * springConstant * displacementM * displacementM0.125 = 0.125
- Calculate Oscillation PeriodOscillation Period = 2 * π * sqrt(massKg / springConstant)0.6283 = 0.6283
- Calculate FrequencyFrequency = 1 / period1.5915 = 1.5915
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