# What is the equation if that projection starts SHM on the $x$-axis from extreme position?

Consider A particle performing Uniform Circular Motion. We know that its projection on diameter performs SHM. Then, if that projection starts SHM on the y axis from mean position, then $$y=A\text{sin}(ωt)$$ if that projection starts SHM on the y axis from extreme position, then $$y=A\text{cos}(ωt)$$ if that projection starts SHM on the x axis from mean position, then $$x=A\text{cos}(ωt)$$ Then What is the equation if that projection starts SHM on the x axis from extreme position?

• Using polar co-ordinates (see the answer below) is the most general approach. But also note that any SHM that starts from an extreme position has equation $\pm A \cos (\omega t)$ and any SHM that starts from the mean position has equation $\pm A \sin (\omega t)$. Commented Mar 19 at 7:07
• Voting to reopen. Clearly a conceptual question not a "do my homework for me" question. Commented Mar 19 at 15:32

$$r = A$$ $$\theta(t) = \omega t + \theta_0$$
where $$\theta_0$$ is the phase at $$t=0$$. Vary $$\theta_0$$ to create the initial position, and convert to Cartesian coordinates to find $$(x(t), y(t))$$.