Study Guides/Physics/Time Period of Simple Pendulum
Study Guide · Physics

Time Period of a Simple Pendulum: Formula and Derivation

A Simple Pendulum consists of a small, heavy ball (bob) suspended from a fixed point by a light, inextensible string. It is the classic example of Simple Harmonic Motion (SHM) studied in Class 11 Physics.

Question (Click to Flip)

What is the formula for the time period of a simple pendulum?

Answer

The time period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. It does not depend on the mass of the bob.

Card 1 of 1 free previews

Key Facts

Formula: T = 2π√(L/g).

Depends on: Length (L) and Gravity (g).

Independent of: Mass of bob and amplitude (for small oscillations).

Isochronism: Same time period for different amplitudes — the principle Galileo discovered.

Formula for Time Period

The time period (T) is the time taken for the pendulum to complete one full oscillation (swing left and return right).

Formula: T = 2π√(L/g)

Where:

  • T = Time period (in seconds)
  • L = Length of the pendulum string (in meters)
  • g = Acceleration due to gravity (9.8 m/s²)
  • π = 3.14159...

What Affects the Time Period?

Factors that DO affect T:

  1. Length (L): Longer pendulum → longer time period. T ∝ √L.
  2. Gravity (g): Higher gravity → shorter time period. T ∝ 1/√g.

Factors that do NOT affect T:

  1. Mass of the bob: Whether the ball is made of wood or iron, it doesn't matter.
  2. Amplitude (how far it swings): For small angles, the time period is constant regardless of amplitude. This is called isochronism.

Questions and Answers

What is the formula for the time period of a simple pendulum?+

The time period of a simple pendulum is given by T = 2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. It does not depend on the mass of the bob.

More in Physics

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.