PhysicsUK Simulation

Simple Harmonic Motion Explorer

Drag, damp and drive an oscillator. Watch displacement, velocity, acceleration and energy respond live — then sweep the driving frequency and find resonance.

OCR A · Module 5 Oscillations AQA · 3.6.1 Periodic motion Damping · Resonance · Energy

Controls

System

Mass m0.50 kg

Spring constant k15.0 N m⁻¹

Amplitude A0.15 m

DampingNone

Damping constant b0.00 N s m⁻¹

Driving force

Periodic driver F₀ cos(2πfₓt)

Display

Velocity vector

Acceleration vector

Try this

Mass & period. Predict first: quadruple m — does T double, halve or stay the same? Now try it.
Moon pendulum. Will a 1 m pendulum swing faster or slower on the Moon? Switch gravity and check T.
Critical damping. Raise damping until the oscillator returns to equilibrium as fast as possible without overshooting. Watch the chip.
Hunt the resonance. Add light damping, switch the driver on, then sweep fₓ slowly through f₀ and watch the marker climb the curve.

Oscillator

Drag the mass, then release

T 1.15 s T (sim) – f 0.87 Hz ω 5.48 rad s⁻¹ x 0.150 m v 0.00 m s⁻¹ a –4.50 m s⁻²

T = 2π√(m/k) = 2π√(0.50 / 15.0) = 1.15 s

Motion graphs

v leads x by T/4 · a is antiphase with x

When x is at a maximum, v is zero — and a is at its largest in the opposite direction.

Energy

Kinetic ½mv²0 mJ

Potential (stored)169 mJ

Total E169 mJ

KE ⇄ PE twice per cycle. With damping, the total drains away as heat — watch the Total bar.

The defining equation

a = −ω²x

A straight line through the origin with negative gradient −ω² — the fingerprint of SHM.

Resonance

Switch on the driving force to explore forced oscillations and resonance.

Amplitude peaks when the driving frequency ≈ natural frequency. More damping → a lower, broader peak at a slightly lower frequency.