Question

A cork floating in a lake is bobbing in simple harmonic motion. Its displacement above the bottom of the lake is modeled by푦=0.2cos20휋푡+8where 푦is measured in meters and 푡is measured in minutes.a) Find the frequency of the motion of the cork. ____________b) Find the maximum displacement of the cork above the lake bottom. ____________

Answer 1

Explanation:

The displacement pf the bob is modeled by the following equation as :

$y=0.2\ cos20\pi t+0.8$..............(1)

The general equation of simple harmonic motion is given by :

$y=A\ cos\ \omega t+\phi$...........(2)

On comparing equation (1) and (2) we get :

(a) $\omega=20\pi$

$\omega=20\pi$        

$2\pi f=20\pi$

f is the frequency of the motion of the cork.

$f=10\ Hz$

(b) In the equation (1), the displacement of the cork is 0.2. So, the maximum displacement of the cork above the lake bottom is 0.2 + 8 = 8.2 meters

Hence, this is the required solution.