Experiment 7: Simple Harmonic Motion - Theory & Concepts - Pendulum

A theory-first treatment of simple harmonic motion, pendulum dynamics, spring oscillations, energy, damping, resonance, graph interpretation, simulations, and laboratory application.

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Simple Pendulum — Exact Numerical Integration

Pendulum Setup

Length (

L

)1.5 m

Mass (

m

)2.0 kg

Initial Angle (

\theta_0

)30°

Damping Ratio (

\zeta

)0.10

Dynamics Equations

Equation of Motion:

\ddot{\theta} + \frac{g}{L}\sin\theta = 0

Small-Angle Period:

T = 2\pi\sqrt{\frac{L}{g}} = 2.457\,\text{s}

θ (current):30.0°

\omega

:0.000 rad/s

T

(current):0.00 s

Normal (

N

):16.99 N

Energy Balance

PE3.94 J

KE0.00 J

Total E₀3.94 J

Phase Portrait (θ, ω)

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Pendulum Setup

Dynamics Equations

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