Hooke’s Law & Harmonic Motion

Explore a spring in motion

  1. Choose a spring and add slotted masses. Total mass includes the 50 g hanger.
  2. Use Settle at equilibrium to stop motion. Read extension from the unloaded reference line to the pointer. At equilibrium, mg = kΔL, so k = mg/ΔL. Convert centimeters to meters.
  3. Choose a displacement, then press Pull & release, or drag the hanger and let go. Arrow keys on the hanger also adjust its displacement; Enter releases it.
  4. Pause to inspect a moment, step forward 0.02 s, or choose slow motion. The graph shows displacement from equilibrium, positive downward. Compare the time between peaks with T = 2π√(m/k).
  5. Try damping, change the mass, or compare springs. Show the spring constant when ready to check your reasoning.

Share opens a fresh lab. There are no worksheets, data-entry areas, or saved observations.

THE EXPERIMENT

Mass-spring system

AT EQUILIBRIUM
RETORT STAND / HELICAL SPRING / SLOTTED MASSESEARTH · 9.81 m/s²
Spring and hanging masses on a laboratory standA calibrated ruler measures spring extension. Drag the mass hanger to displace the spring. cmUnloaded endEquilibrium DRAG HANGER TO PULL & RELEASECAST IRON RETORT STANDSIMULATION TIME / s0.00DIGITAL TIMER
Total mass
Equilibrium extension
Weight, mg
Displacement ↓

At equilibrium. Add mass to stretch the spring, or pull and release to start oscillating.

WATCH THE PATTERN

Position vs. time

Last 8 simulation seconds
Live displacement from equilibrium versus timePositive displacement is downward. An ideal oscillation traces a sine wave.

Position is measured from equilibrium, not the unloaded spring. Pause the lab to freeze both the apparatus and graph.

Physics behind the bench

At equilibrium: mg = kΔL. During motion: mÿ + bẏ + ky = 0, where y is displacement from equilibrium. With no damping, T = 2π√(m/k). Springs A, B, and C have constants of 10, 20, and 30 N/m. The massless spring is ideal and stays elastic throughout this lab’s range. The hanger contributes 50 g. Real springs have mass and an elastic limit; excessive loading can permanently deform them.

The ruler’s zero aligns with the unloaded spring end; its pointer tracks the loaded end. Equipment is illustrated to scale along the motion axis; weights are enlarged for visibility. Changing spring, mass, or damping starts a fresh motion trace. No measurements are stored.