How to use (3 steps)
- Choose Spring or Pendulum and keep the sample values or enter your own.
- For the spring, enter mass m, spring constant k, amplitude A, and optional time t. For the pendulum, enter length L, gravity g, and an amplitude angle (Earth and Moon presets are one tap).
- Press Compute to view ω, period, frequency, peak speed/acceleration/energy, and a step-by-step breakdown for each mode.
Key formulas: spring ω = √(k/m); pendulum ω = √(g/L) (small-angle approximation).
Inputs
Results
Results update after you compute. Values are formatted for quick inspection.
How it's calculated
Using the SHM modes
This page covers spring motion and the small-angle pendulum. Pick the mode that matches your system first, because the required inputs and interpretation notes are different.
Suggested workflow
- For a spring-mass system, enter m and k to get the period and frequency.
- For a pendulum, enter the length and local gravity, then treat large amplitudes as an approximation warning rather than an exact period prediction.
- Use the note under the result to see whether the small-angle assumption is still reasonable.
What the page assumes
The spring mode assumes an ideal Hooke's-law spring and no damping. The pendulum mode uses the standard small-angle approximation, so the warning becomes important once the release angle is no longer small.
Common mistakes to avoid
- Entering amplitude in the pendulum mode and expecting the period to stay exact at large angles.
- Mixing linear displacement with angular displacement between the two modes.
- Using rounded output values as if they were measured experimental data.
See also
FAQ
What is simple harmonic motion?
Simple harmonic motion is a repeating oscillation where the restoring force is proportional to displacement. Mass–spring systems and small-angle pendulums are classic examples.
Does pendulum period change with amplitude?
In the small-angle approximation used here, the period is nearly independent of amplitude. Large swings deviate and the actual period becomes slightly longer.
How do mass and spring constant affect the period?
For a spring–mass system, T = 2π√(m/k). Heavier masses oscillate more slowly, and stiffer springs (larger k) oscillate faster.
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