Question #f1ade
1 Answer
see below
Explanation:
A linear restorative force is a key ingredient of shm. So in a spring system, the spring forces the mass back toward the centre. Thus
The solution to the related differential equations are sinusoids, typically stated as:
Uniform circular motion is a different thing. There is no restorative force in the sense that the mass is always a distance/radius
And that force is constant in magnitude, but changes direction as it is always centre-seeking force ... in the sense that there is a centrifugal force that causes the mass to accelerate towards the centre of the circle.
You can connect them up by projecting uniform circular motion onto a straight line. For convenience, the x or y axis
Uniform circular motion of fixed radius
Projecting this onto the x-axis using the dot product....
So the motion of the projection is sinusoidal.
You can compare this directly to