# Thread: The Motion Of a Pendulum

1. ## The Motion Of a Pendulum

The motion of an pendulum can be modeled by the function
f(t) = 10cos(2t) * 0.95^t, where f is the horizontal displacement from the rest position, in centimeters, as a function of time, t, in seconds. What is the length of the pendulum?

I made two triangles, one with base 10 cm and another with base 8.48 because that is how far the pendulum travels when it returns. I couldn't figure out what to do from there. The answer in the back is 245 cm.

2. The period is $\displaystyle 10\pi$

So, using the formula $\displaystyle T=2\pi\cdot\sqrt{\frac{L}{g}}$

solve for L.

$\displaystyle 10\pi=2\pi\cdot\sqrt{\frac{L}{9.8}}$