Question

Harmonic motion help please (:

find a model for simple harmonic motion if the position at t=0 is 0 the amp is 3 centimeters and the period is 2 seconds

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

Answer 1

A. part is correct

Answer 2

Simple Harmonic Motion is represented either as a sine or a cosine function.
Here, at t = 0, position = 0 which indicates a sine wave.
y = Asin(Bt)
where A is the amplitude and B = (2*pi) / period

Answer 3

\[x(t)=A*sin(\omega*t+\theta)\]\[A=3~cm\\\omega=\frac{2\pi}{T}=\pi\\\theta=0\]Replacing\[x(t)=3*sin(\pi*t)\]And the function when the t=0 is 0, once the function of harmonic motion could be too\[x(t)=A*cos(\omega*t+\theta)\]And i can prove it if necessary.

Answer 4

Thank you (: