Simple Harmonic Motion Part 1.docx

Simple Harmonic Motion Definition: A body is in simple harmonic motion if its acceleration , a is directly proportional to its displacement, x from a fixed point and is always directed towards that point,0.

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Acceleration a= - w x, where w is a constant a (Note : the negative=sign shown that the acceleration always toward equilibrium position. - ) w x , Graph of acceleration against displacement (a-x)

________________________________________________________ Amplitude：Maximum distance from the equilibrium Period: Time taken for a complete oscillation Frequency: The number of oscillation per second Angular frequency: Product of the frequency of oscillation and 2π radian Angular frequency, w= 2πf Frequency, f = Period, T=

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Displacement and time 2

From the definition of simple harmonic motion,acceleration a= - w x a is a second order differential equation. Its general equation is = w or x , ________________________________________________________

When

________________________________________________ Then

and

__________________________________________________ So, we can find out that 1) velocity v leads displacement x by π/2 rad. 2) Acceleration a in the anti phase with displacement x, phase difference=-π radians.

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