Explanation

The time period of a simple pendulum is given by:

This shows no dependence on mass because:

• The restoring force (F = -mg sinθ) is proportional to mass
• The inertia (resistance to motion) is also proportional to mass
• These two effects cancel each other out

Try changing the mass in the simulation - you'll see the period remains constant!

Explanation

For small angles (θ < 15°), we approximate sinθ ≈ θ, giving:

This results in simple harmonic motion with period:

For larger angles:

• sinθ > θ, so the restoring force is weaker than the linear approximation
• This effectively reduces the "g" in the period formula
• Resulting in a longer period: T > 2π√(l/g)

Try increasing the initial angle in the simulation to observe this effect!

Explanation

Wristwatch in free-fall:

• Mechanical watches use springs, not gravity
• They keep accurate time regardless of free-fall
• Demonstrated by the working watch in the right simulation

Pendulum in free-falling cabin:

• The effective gravity becomes g - g = 0
• No restoring force acts on the pendulum
• Frequency becomes zero (no oscillation)
• Select "Free-Falling Cabin" scenario to observe