Equations for Simple Harmonic Motion
Let’s consider a particle of mass (m) doing Simple Harmonic Motion along a path A’OA the mean position is O. Let the speed of the particle be V0 when it is at position P (at some distance from point O)
At the time, t = 0 the particle at P (moving towards point A)
At the time, t = t the particle is at Q (at a distance X from point O) at this point if velocity is V then:
The force F acting on a particle at point p is given as,
F = -K X [where, K = positive constant]
We know that,
F = m a [where, a = Acceleration at Q]
⇒ m a = -K x
⇒ a = -(K/m) x
As K/m = ω2
Thus, a = -ω2x
Also, we know a = d2X/d2t]
Therefore, d2x/d2t = -ω2x
d2x/d2t + ω2x = 0
which is the differential equation for linear simple harmonic motion.
Simple Harmonic Motion
Simple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the membrane in drums and diaphragms in telephone and speaker system creates the precise sound. Understanding Simple Harmonic Motion is key to understanding these phenomena.
In this article, we will grasp the concept of Simple Harmonic Motion (SHM), its examples in real life, the equation, and how it is different from periodic motion.
Table of Content
- SHM Definition
- Types of Simple Harmonic Motion
- Equations for Simple Harmonic Motion
- Solutions of Differential Equations of SHM
- SHM JEE Mains Questions