Thursday, April 24, 2008

Concept review Ch. 12 Simple Harmonic Motion

Simple harmonic motion is a special type of oscillation in which the particle oscillates on a straight line, the acceleration of the particle is always directed towards a fixed point on the line and its magnitude is proportional to the displacement of the particle from this point.

The fixed point is called centre of oscillation.

If we take centre of oscillation as the origin and the line of motion as the X axis, SHM can be defined by the equation

a = -ω²x ... (1)

Where ω² is a positive constant.
If x is positive, a is negative and if x is negative, a is positive. It means that the acceleration if always directed towards to the centre of oscillation.

As acceleration is; a = F/m

We can write SHM equation as
F/m = -ω²x
F = -mω²x
F = -kx ...(2)

Force constant or spring constant
The constant k = mω² is called the force constant or spring constant.

The resultant force on the particle is zero when it is at the centre of oscillation

Equation of motion of SHM

Terms Associated with SHM

a. Amplitude
b. Time period
c. Frequency and angular frequency
d. Phase
e. Phase constant

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