A body in oscillatory motion whose acceleration is directly proportional to displacement and is always directed towards mean position is called simple harmonic motion. Here we are going to derive equations for velocity and acceleration of body in SHM.
Simple harmonic motion is the projection of uniform circular motion on a diameter of the circle in which the latter motion takes place.
A particle in SHM will have a displacement y represented as y = a cos(wt) whose initial phase is equal to zero. Here the particle is in horizontal circular motion. If it is in vertical circular motion instead of sin function we have to use cosine function.By differentiating the above equation we will get velocity and by differentiating once again we will get the equation for acceleration.
Acceleration can be determined further with equation – ω^2 A cos ( ωt + φ) or – ω^2 (t)
Its graphical method we can represent displacement ,velocity and acceleration as shown below.
SHM related topics
Time Period of Simple pendulum
What is periodic and Oscillatory Motion is ?
Displacement in Oscillatory motion
Simple Harmonic Motion
Topics of Heat and Thermodynamics
Heat engine
Internal Energy
Zeroth law of thermodynamics
Thermodynamics Introduction
Heat transfer by radiation
Heat transfer by convection
Heat transfer and conduction
Heat and Temperature
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