Oscillations · Simple Harmonic Motion

Mass–Spring Lab

T = 2π√(m/k)

ω = 5.00 rad s⁻¹T = 1.26 sf = 0.796 Hz

v max — passing equilibrium

a max — at extreme, restoring toward centre

drag — orbit · scroll — zoom

Try first: slide Amplitude — T never changes.

Controls

Mass m1.00 kg

Spring constant k25 N m⁻¹

Amplitude x₀0.30 m

Damping b0.00 kg s⁻¹

m, k, x₀ restart from rest; b applies live; x positive downward.

x / m

0.300

v / m s⁻¹

0.000

a / m s⁻²

-7.50

KE½mv²

0.000 J

PE½kx²

1.13 J

TotalKE + PE

1.13 J

ⓘ more

PE is elastic, measured about equilibrium. E₀ = ½kx₀² = 1.13J. With b = 0 the Total bar stays constant; with b > 0 it decays.

What to notice

v leads x by π/2 (a quarter period). v is greatest as the block passes equilibrium and zero at the extremes — watch the graphs.
a is antiphase with x. a = −ω²x: acceleration is largest at the extremes and always points back toward equilibrium.
Isochronism. Change x₀ and T does not change — amplitude never appears in T = 2π√(m/k).
g does not appear. A vertical spring has the same period as a horizontal one: gravity only shifts the equilibrium position, not the restoring force per unit displacement.
Add damping. With b > 0, x(t) decays inside an exponential envelope and the Total energy bar falls.