# Uniform
Circular motion’s one dimensional projection

Simple
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 $$ d 2 x d t 2 = - ω 2 x and $\frac{{d}^{}}{}$ 2 y d t 2 = - ω 2 y respectively.

## Youtube:

http://youtu.be/0IaKcqRw_Ts This video shows how
a pendulum's oscillations and the shadow of rotating object are
related. This could be used to demonstrate that the projection of
a circular motion is actually a simple harmonic motion.

## Run
Model:

https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHMcircle/SHMcircle_Simulation.html