Find a model for simple harmonic motion if the position at t = 0 is 0, the amplitude is 3 centimeters, and the period is 2 seconds.

Question

anonymous · Answer

A. d = 3cos(πt)
B. d = 3sin(πt)
C. d = 3sin(π/2 * t)
D. d = 2cos(3t)

anonymous · Answer

$$d(t)=Asin(\frac{ 2\pi }{ T}t+\phi_0)$$$$d(0)=Asin(\phi_0)=0\rightarrow \phi_0=0$$$$d_{\max}=A=3$$
$$T=2 \rightarrow d(t)=3\sin(\frac{ 2\pi }{ 2}t)=3\sin(\pi t)$$

anonymous · Answer

Thanks! :) Really appreciate it

anonymous · Answer

you are welcome. The important thing is that you get the reasoning behind rather than just the solution

anonymous · Answer

What you have given is definitely more than just the solution. Great to see how to get this answer in the first place