1. What is the Pendulum Force Equation?

The pendulum force equation calculates the restoring force acting on a pendulum bob. The force is given by \( F = -m \times g \times \sin(\theta) \), where m is mass, g is gravity, and θ is the angular displacement from the vertical.

2. How Does the Calculator Work?

The calculator uses the pendulum force equation:

Where:

• \( m \) — Mass of the pendulum bob (kg)
• \( g \) — Acceleration due to gravity (m/s²)
• \( \theta \) — Angular displacement from vertical (radians)

Explanation: The negative sign indicates that the force acts in the opposite direction to the displacement, acting as a restoring force toward the equilibrium position.

3. Importance of Pendulum Force Calculation

Details: Calculating pendulum force is essential for understanding oscillatory motion, designing pendulum-based systems, and analyzing harmonic motion in physics and engineering applications.

4. Using the Calculator

Tips: Enter mass in kilograms, gravity in m/s² (Earth's gravity is approximately 9.81 m/s²), and angle in radians. All values must be valid (mass > 0, gravity > 0).

5. Frequently Asked Questions (FAQ)

Q1: Why is the force negative in the equation?
A: The negative sign indicates that the force is a restoring force, always acting toward the equilibrium position opposite to the displacement direction.

Q2: What is the small angle approximation?
A: For small angles (θ < 0.2 rad), sin(θ) ≈ θ, simplifying the equation to F = -m × g × θ, which results in simple harmonic motion.

Q3: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 30° = 30 × π/180 ≈ 0.5236 radians.

Q4: Does this equation account for air resistance?
A: No, this is the ideal pendulum equation that assumes no air resistance or friction at the pivot point.

Q5: What is the period of a pendulum?
A: For small angles, the period T = 2π√(L/g), where L is the pendulum length. The force equation helps derive this period formula.