Procedure

1. Use sliders to set up the pendulum length, mass, and initial angle.
2. Click the release button to observe the pendulum swinging.
   Data for angular displacement (θ), velocity (v), and energies (KE, PE, TME) will be recorded.
3. View real-time graphs of:
   • Total Mechanical Energy (TME) vs. time,
   • Kinetic Energy (KE) vs. time,
   • Potential Energy (PE) vs. time.
4. Verify energy conservation by checking if the total mechanical energy (TME) remains constant throughout the motion.
5. Adjust inputs (length, mass, initial angle) and rerun the simulation to observe how the behavior changes.
6. Save graphs and results for reporting or further analysis.

Formulae for Simulation

1. Height (h)

The vertical height (h) of the pendulum bob relative to its lowest point is given by:

h = L(1 - cos(θ))

Where:

• L = Length of the pendulum (in meters),
• θ = Angular displacement (in radians).

2. Velocity (v)

The instantaneous velocity (v) of the pendulum bob at an angular displacement θ is given by:

v = √(2gL(cos(θ) - cos(θ₀)))

Where:

• g = Acceleration due to gravity (9.81 m/s²),
• L = Length of the pendulum (in meters),
• θ = Angular displacement at time t (in radians),
• θ₀ = Initial angular displacement (in radians).