Spring-Mass System — x = A·cos(ωt)
Drag amplitude and spring constant. Watch the oscillation live.
Amplitude A 50 cm
Spring const k 10 N/m
Mass m 2 kg
ω = √(k/m) = rad/s  |   T = 2π/ω = s
Angular freq ω
rad/s
Period T
s
Frequency f
Hz
Max speed
m/s
Max force
N

x–t (displacement over time)

Phase diagram (x vs v)

Period vs mass

Period vs spring k

Simple Pendulum — T = 2π√(L/g)
Change length and gravity. Notice that mass doesn't affect period!
Length L 1.0 m
Gravity g 9.8 m/s²
Max angle θ₀ 20°
T = 2π√(L/g) = s  |   f = Hz
Length L
m
Gravity g
m/s²
Period T
s
Frequency f
Hz
Max speed
m/s

Angle over time

T vs Length

Energy in SHM — KE + PE = constant
Watch kinetic and potential energy trade off as the mass oscillates.
Amplitude A 40 cm
Spring k 20 N/m
Mass m 2 kg
E_total = ½kA² = KE + PE = J
Total Energy E
J
Max KE
J
Max PE
J
Max speed v_max
m/s

KE, PE and total energy over time

Energy vs displacement

Wave Motion — v = fλ
Combine frequency, wavelength, and amplitude. See the wave travel live.
Frequency f 2 Hz
Wavelength λ 3 m
Amplitude A 40 cm
v = fλ = m/s  |   T = 1/f = s
Wave speed v
m/s
Frequency f
Hz
Wavelength λ
m
Period T
s
Wave number k
rad/m

Displacement at x=0 over time

Snapshot: displacement vs position