SATHEE: Introduction To Simple Harmonic Motion

Introduction To Simple Harmonic Motion

Concepts to remember on Introduction to Simple Harmonic Motion for JEE and CBSE board exams:

SHM: Periodic motion where restoring force is ∝ -ve displacement from mean position.

Displacement of particle executing SHM: $x = A \cos (ω t + ϕ) .$
Velocity of particle executing SHM: $v = - A ω \sin (ω t + ϕ) .$
Acceleration of particle executing SHM: $a = - A ω^{2} \cos (ω t + ϕ) .$

Time period of SHM: $T = 2 π / ω .$
Frequency of SHM: $f = ω / 2 π .$
Amplitude of SHM: Maximum displacement from the mean position.
Phase angle of SHM: Angle between the initial position of particle and the positive direction of the displacement axis at time t= 0.
Energy of a particle executing SHM: $E = \frac{1}{2} k A^{2}$
Potential energy of a particle executing SHM: $U = \frac{1}{2} k x^{2} .$
Kinetic energy of a particle executing SHM: $K = E - U = \frac{1}{2} k A^{2} (1 - \cos^{2} ω t) .$

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Introduction To Simple Harmonic Motion

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