Pendulum Force Calculator With Time

Pendulum Force Equation:

\[ F = m \times g \times \sin\left(\frac{2 \pi t}{T}\right) \]

Mass (m):

Gravity (g):

m/s²

Time (t):

Period (T):

Pendulum Force (F):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Pendulum Force Equation?

The pendulum force equation calculates the restoring force acting on a pendulum at any given time. It describes how the force varies sinusoidally with time as the pendulum oscillates.

2. How Does the Calculator Work?

The calculator uses the pendulum force equation:

\[ F = m \times g \times \sin\left(\frac{2 \pi t}{T}\right) \]

Where:

\( F \) — Pendulum force (N)
\( m \) — Mass of the pendulum bob (kg)
\( g \) — Acceleration due to gravity (m/s²)
\( t \) — Time elapsed (s)
\( T \) — Period of oscillation (s)

Explanation: The equation calculates the component of gravitational force that acts as the restoring force along the pendulum's arc of motion at any given time.

3. Importance of Pendulum Force Calculation

Details: Understanding pendulum forces is crucial for analyzing oscillatory motion, designing pendulum clocks, studying harmonic motion, and various engineering applications involving periodic systems.

4. Using the Calculator

Tips: Enter mass in kilograms, gravity in m/s² (9.8 for Earth), time in seconds, and period in seconds. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum force experienced by the pendulum?
A: The maximum force occurs when sin(2πt/T) = ±1, giving F_max = m × g. This happens at the extreme positions of the swing.

Q2: How does the period affect the force calculation?
A: The period determines the frequency of oscillation. A shorter period means faster oscillations and more rapid force changes.

Q3: What value should I use for gravity?
A: Use 9.8 m/s² for Earth's surface. For other locations or planets, use the appropriate gravitational acceleration value.

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: Can this be used for large amplitude swings?
A: This equation is most accurate for small angles (less than 15°). For larger amplitudes, the motion becomes non-linear and more complex equations are needed.