Pendulum Calculator

Category: Chemistry
- May 22, 2025
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Calculate various properties of a pendulum including period, frequency, and maximum velocity. This calculator helps with physics problems related to simple harmonic motion.

Pendulum Type

Simple Pendulum Parameters
°

Angle from vertical (less than 10° for small-angle approximation)

m/s²

Default: Earth's gravity (9.81 m/s²)

Damping Options

Output Settings

About Pendulums

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced from its resting equilibrium position, it oscillates due to the restoring force of gravity.

Simple Pendulum

A simple pendulum consists of a mass (called a bob) attached to a massless string or rod. When the angle of displacement is small, the period of oscillation is independent of the amplitude.

  • Period: T = 2π√(L/g)
  • Frequency: f = 1/T = 1/(2π)·√(g/L)
  • Angular Frequency: ω = 2πf = √(g/L)
Physical Pendulum

A physical pendulum has an extended mass distribution rather than a point mass. The period depends on the moment of inertia and the distance to the center of mass.

  • Period: T = 2π√(I/(m·g·d))
  • Frequency: f = 1/T = 1/(2π)·√(m·g·d/I)
  • Angular Frequency: ω = 2πf = √(m·g·d/I)
Spring Pendulum

A spring pendulum consists of a mass attached to a spring. Its motion follows simple harmonic motion with the restoring force provided by the spring.

  • Period: T = 2π√(m/k)
  • Frequency: f = 1/T = 1/(2π)·√(k/m)
  • Angular Frequency: ω = 2πf = √(k/m)
Damped Pendulum

In real-world pendulums, damping forces like air resistance and friction cause the amplitude to decrease over time.

  • Underdamped: The pendulum oscillates with decreasing amplitude
  • Critically Damped: The pendulum returns to equilibrium in minimum time without oscillating
  • Overdamped: The pendulum returns to equilibrium without oscillating, but slower than critical damping
Energy in Pendulums

In an ideal pendulum, energy is conserved and continuously transforms between potential and kinetic energy.

  • Potential Energy: Highest at maximum displacement (maximum amplitude)
  • Kinetic Energy: Highest when passing through the equilibrium position
  • Total Energy: Remains constant in an ideal system without damping
Applications of Pendulums
  • Timekeeping: Pendulum clocks were historically very accurate timepieces
  • Seismometers: Used to detect and measure earthquakes
  • Demonstration of Earth's Rotation: Foucault pendulum
  • Engineering: Analysis of oscillatory systems and structural vibrations
  • Physics Education: Demonstrating principles of mechanics, harmonic motion, and energy conservation

Understanding the Pendulum Calculator

The Pendulum Calculator is a handy tool designed for those curious about the Physics of pendulums. Whether you're a student tackling homework or just someone interested in how pendulums work, this calculator helps you find various properties. You can easily calculate the period, frequency, and maximum velocity of different types of pendulums.

Types of Pendulums You Can Calculate

This calculator allows you to choose between three types of pendulums: simple, physical, and spring. Each type has its unique characteristics and formulas. You can select the one that fits your study or project needs.

Simple Pendulum Parameters

  • Length (L): The distance from the pivot point to the center of mass of the bob.
  • Amplitude (A): The maximum distance from the rest position.
  • Initial Angle (θ): The angle at which the pendulum is released.
  • Gravitational Acceleration (g): Usually set to Earth's gravity, which is approximately 9.81 m/s².

These parameters are crucial for accurate calculations. Adjust them based on your specific experiment or problem.

Physical and Spring Pendulum Inputs

For physical pendulums, you will need to input the moment of inertia and the distance to the center of mass. For spring pendulums, the spring constant and the mass of the object are important. Each pendulum type has inputs tailored to its unique motion characteristics, ensuring you get precise results.

Advanced Features: Damping Options

The Pendulum Calculator also includes advanced features like damping options. You can choose to include damping in your calculations to simulate real-world conditions. Damping affects how the pendulum moves over time, making this feature valuable for more complex studies.

Visualizing Pendulum Motion

The calculator provides an option to visualize pendulum motion. This feature helps you see how the pendulum swings over time. You can play and reset the animation, making it easier to grasp the concept of pendulum oscillations.

Energy Calculations in Pendulums

  • Maximum Kinetic Energy: The energy when the pendulum is at its lowest point.
  • Maximum Potential Energy: The energy at the highest point of the swing.
  • Total Energy: The sum of kinetic and potential energy, illustrating conservation in an ideal system.

Understanding energy in pendulums is key to grasping their behavior. The calculator provides these important energy values so you can study them closely.

Why Use the Pendulum Calculator?

The Pendulum Calculator is perfect for students, teachers, and Science enthusiasts. It simplifies complex calculations and enhances understanding through visualization and detailed results. By using this tool, you can deepen your knowledge of pendulum physics while saving time on calculations.