Simple Harmonic Motion (SHM) Lab - Physics Simulations

t = 0.00s

Pendulum Energy

Spring Energy

Live Telemetry & Summary

Observe the live period calculations and angular/linear displacements. Tweak parameters to adjust oscillation speed.

Pendulum Period (T_p):3.17 s

Spring Period (T_s):1.78 s

Pendulum angle (θ):30.0°

Spring displacement (x):0.50 m

Variable Adjuster

Pendulum Length (L)2.5m

Gravity (g)9.8m/s²

520

Spring Mass (m)2kg

0.55

Spring Constant (k)25N/m

1050

Simple Harmonic Motion Lab

OSCI

Simple Harmonic Motion (SHM) occurs when the restoring force is directly proportional to displacement. In a gravity pendulum, this restoring force is the gravity component tangential to swing. In a mass-spring system, it is Hooke's Law (F = -kx). Both systems oscillate periodically, converting Potential Energy (PE) at the peaks entirely into Kinetic Energy (KE) at the equilibrium center.

T_{pend} = 2\pi \sqrt{\frac{L}{g}}, \quad T_{spring} = 2\pi \sqrt{\frac{m}{k}}

Whiteboard Solver Steps

Step 1

Simple Gravity Pendulum Period

For small angles, the swinging period of a pendulum depends solely on its length and the gravitational acceleration, not on the mass of the bob.

T_{pendulum} = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{2.5}{9.8}} = 3.17 \text{ s}

Step 2

Mass-Spring Harmonic Period

The period of a mass-spring oscillator is determined by the mass inertia and the stiffness constant k of the spring.

T_{spring} = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{2}{25}} = 1.78 \text{ s}

Step 3

Simple Harmonic Motion Equations

The restoring forces (gravity component for pendulum, Hooke's Law force F = -kx for spring) lead to pure sinusoidal motion over time.

\theta(t) = \theta_0 \cos(\omega_p t), \quad x(t) = A \cos(\omega_s t)

RV Anveshana