Hooke’s Law & Harmonic Motion

Explore a spring in motion

Determine k from the slope of force against extension. Then test how mass and amplitude affect the period.

  1. Choose a spring and add slotted masses. Total mass includes the 50 g hanger.
  2. Use Settle at equilibrium to stop motion. The force-extension graph shows the equilibrium relationship; the dot follows your selected mass. 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. The graph shows roughly four cycles. After two complete cycles, a bracket measures the time between successive peaks. Compare this measured period 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

Force vs. extension

At equilibrium

What to look for

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

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). Reveal the spring constant to check a value you determine from force and extension. The spring can both stretch and compress in this ideal model. 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.