Trigonometry

Question

A ball on a spring is pulled 5 inches above its rest position and then released.The period of the motion is 10 sec. Write the equation for the ball's simple harmonic motion. 

Answer 1

Brian, since we are starting up on the y-axis, this is cosine, and the equation for cosine is y = acos(bx), where a is the amplitude and b plays into the period.

 

The period is 10, and period = 2pi/b, so...

10 = 2pi/b

10b = 2pi

b = pi/5

 

Our equation is y = 5cos(pi/5)

 

Hope this helps!