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Pendulum Lab
Status
Ready
Simple
Damped
Parameters
Length (L)
2.0 m
Mass (m)
1.0 kg
Initial Angle (θ₀)
30°
Damping (b)
0.3
Gravity
Earth — 9.81 m/s²
Moon — 1.62 m/s²
Mars — 3.72 m/s²
Jupiter — 24.79 m/s²
Options
Motion Trail
Force Vectors
Slow Motion (0.25×)
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📐 Equations & Results
Period
T=2π√(L/g)
0.00
s
Frequency
f=1/T
0.00
Hz
ω₀
√(g/L)
0.00
rad/s
ω_d
√(ω₀²−γ²)
0.00
rad/s
γ
b/(2mL²)
0.00
1/s
Angle
θ
0.00
°
Angular Vel.
ω
0.00
rad/s
Tan. Velocity
v=Lω
0.00
m/s
Kinetic E.
½mL²ω²
0.00
J
Potential E.
mgL(1−cosθ)
0.00
J
Total Energy
KE+PE
0.00
J
Tension
mgcosθ+mLω²
0.00
N
Torque
τ = −mgLsinθ
0.00
N·m
Tangential F.
Fₜ = −mgsinθ
0.00
N
Normal F.
Fₙ = mLω²
0.00
N
📖 Governing Equations
EOM:
θ̈ = −(g/L)sinθ − 2γθ̇
Period:
T = 2π√(L/g)
Simple:
θ(t) = θ₀cos(ω₀t)
Damped:
θ(t) = θ₀e
−γt
cos(ω
d
t)
ω₀
= √(g/L) |
ω
d
= √(ω₀²−γ²)
γ
= b/(2mL²)
KE
= ½mL²ω² |
PE
= mgL(1−cosθ)
T
= mgcosθ + mLω²
Fₜ
= −mgsinθ |
Fₙ
= mLω²
Phase Space (θ vs ω)
Energy Distribution