Sat February 23, 2013 By:

maam im really confused. I dont understand that in the equation for simple harmonic motion, while describing the position of a particle along the X axis or Y axis, where do we use the sine and cos notations and when do we put a negative sign inside the brackets for phase and how to identify whether the motion is clockwise or anticlockwise. Can u please make all the types of equations clear to me?

Expert Reply
Tue February 26, 2013
the first thing about the simple harmonic equation is its differential equation:
d2x/dt2 = -w2x
here we take w as the frequency of oscillations.
since this equation represents a periodic motion so we can represent it by a sin or cos function. Any of them can be used.
they are taken as:  y = sin (wt + ?)
for a particle oscillating in y direction
here ? denotes the phase i.e. if the particle is not at y = 0 at t = 0.
thus is calculated using the boundary conditions.
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