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PHYSICS • OSCILLATIONS

Spring,Mass System

Measure simple harmonic motion like a laboratory instrument: scrub phase, inspect force and energy, compare masses and tune the oscillator to a target period.

● LIVE OSCILLATORIdeal Hooke’s-law motion
0.00 s
Period0.00 s
Frequency0.00 Hz
Reference period0.00 s
Target error0.00 s
Maximum speed0.00 m/s
Total energy0.00 J

Oscillation diagnostics

displacement-time + phase portrait

Use the oscillator as a measurement instrument

Scrub through one cycle and watch restoring force, acceleration and velocity change sign. Compare a second mass on the same spring, then inspect how kinetic and elastic potential energy exchange while total energy stays constant.

Fast investigations

  1. Double the mass and test the √m period relationship.
  2. Hold mass fixed and quadruple k to test the inverse √k relationship.
  3. Change amplitude and verify that the ideal period stays unchanged.
  4. Pause at equilibrium and compare maximum speed with maximum kinetic energy.

LEARN WITH THE SIMULATION

Understand Spring,Mass System by experimenting.

START HERE

A mass attached to an ideal spring can undergo simple harmonic motion. Hooke’s law makes the restoring force proportional to displacement, producing a sinusoidal motion whose frequency is set by mass and spring stiffness.

BUILD THE IDEA

What you should understand first

  • Connect Hooke’s law to restoring force.
  • See how mass and spring constant determine frequency.
  • Track the exchange between kinetic and elastic potential energy.

TRY IT YOURSELF

Which change raises the oscillation frequency more: increasing stiffness or increasing mass?

  1. Record frequency for the default system.
  2. Increase the spring constant while holding mass fixed.
  3. Return to default and increase mass instead; compare the directions of change.
Read the visual:

Stiffer springs oscillate faster, while larger masses oscillate more slowly. Frequency scales with √(k/m).

WHY IT WORKS 01

Connect Hooke’s law to restoring force.

A mass attached to an ideal spring can undergo simple harmonic motion. Hooke’s law makes the restoring force proportional to displacement, producing a sinusoidal motion whose frequency is set by mass and spring stiffness. Focus on the relationship between the controlled variable and the measured response rather than treating the visual change as the explanation.

WHY IT WORKS 02

See how mass and spring constant determine frequency.

Stiffer springs oscillate faster, while larger masses oscillate more slowly. Frequency scales with √(k/m). Use an extreme or boundary setting after the baseline trial to check whether the same reasoning still holds.

DO NOT MIX THESE UP

Common misconception

The restoring force points toward equilibrium. Amplitude changes energy but not the ideal natural frequency. Real springs can introduce damping and nonlinearity that this model omits.

PRACTICE CHALLENGE

Which change raises the oscillation frequency more: increasing stiffness or increasing mass?

  • Record frequency for the default system.
  • Increase the spring constant while holding mass fixed.
  • Return to default and increase mass instead; compare the directions of change.
Reveal the reasoning

Stiffer springs oscillate faster, while larger masses oscillate more slowly. Frequency scales with √(k/m). The restoring force points toward equilibrium. Amplitude changes energy but not the ideal natural frequency. Real springs can introduce damping and nonlinearity that this model omits.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • The spring obeys Hooke’s law over the simulated displacement range.
  • The attached mass is concentrated at one point.
  • Spring mass, friction and damping are neglected unless explicitly represented by a control.

Model limitations

  • Real springs become nonlinear outside their elastic range.
  • Energy losses, spring inertia and material hysteresis are not captured.

CONNECT IT

Where this matters

  • Vehicle suspension
  • Vibration isolation
  • Mechanical resonators

WORDS THAT MATTER

Key vocabulary

Spring constant
Measure of spring stiffness.
Restoring force
Force directed toward equilibrium.
Simple harmonic motion
Oscillation produced by a linear restoring force.