Simple harmonic motion can in some cases be considered to be the one-dimensional projection of uniform circular motion . If an object...
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=Asinωt
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=Acosωt for top position or y=−Acosωt 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=Acosωt and y=asinωt each follow the defining relationship for SHM as ordinary differential equations of d2xdt2=−ω2x and d2ydt2=−ω2y respectively.
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