What is a Simple Pendulum?
A simple pendulum is a theoretical mass tied to a massless thread or rod that may swing back and forth in response to gravity. It is an idealized model used in physics to analyze the behavior of oscillating systems. A basic pendulum’s motion is periodic and can be defined by its period, which is determined solely by the length of the string and the acceleration due to gravity.
SHM Equation of Pendulum
Using Newton’s second law and the small-angle approximation, the equation for simple harmonic motion (SHM) of a simple pendulum may be constructed. As a consequence, the equation is:
θ”(t) + (g/L)θ(t) = 0
where
(t) is the angular displacement of the pendulum from its equilibrium position at time t,
g is the gravitational acceleration,
L is the pendulum’s length.
This second-order differential equation can be solved using calculus techniques such as the method of indeterminate coefficients or the method of parameter variation. The generic solution to the equation of motion is as follows:
φ(t) = A sin(t + ∅)
where
A is the motion’s amplitude
This equation expresses the SHM of a basic pendulum with a period
T = 2π√(L/g)
f = 1/T
f = (1/2π)√(g/L)
Physical Pendulum
A rigid body that is capable of rotating around an axis makes up a physical pendulum, a particular kind of pendulum. The physical pendulum can be shaped into a straight rod, a rectangular plate, or a circular disc, in contrast to a basic pendulum, which consists of a tiny mass hanging by a string. The moment of inertia, the separation between the pivot point and the center of mass, and the gravitational pull all affect how a physical pendulum swings.
Table of Content
- What is a Simple Pendulum?
- Physical Pendulum
- Difference between Simple & Physical Pendulum
- How to use Physical Pendulum Formula?
- Solved Examples on Physical Pendulum