Example 3: Uniform Circular motion’s one dimensional projectionSimple harmonic motion can in some cases be considered to be the one-dimensional projection of uniform circular motion. If an object moves with angular speed ω around a circle of radius A centered at the origin of the x−y plane, then its motion along each coordinate is simple harmonic motion with amplitude A and angular frequency ω.
Q1: given that, a circular motion can be described by x = A cos(ω t) and y A sin(ω t) what is the y-component model-equation that can describe the motion of a uniform circular motion?A1: y = Asin (ωt)
Q2: When the x-component of the circular motion is modelled by x = A cos(ω t) and y A sin(ω t) suggest an model-equation for y.A2: y = Acos (ωt) for top position or y = - Acos (ωt) for bottom position
Q3: explain why are the models for both x and y projection of a uniform circular motion, a simple harmonic motion?A3: both x = A cos(ω t) and y A sin(ω t) each follow the defining relationship for SHM as ordinary differential equations of and respectively.