A spider sits on its web, undergoing simple harmonic motion with amplitude A.What fraction of each cycle does the spider spend at positions with x>0.75A? Hint: Use the analog of uniform circular motion.

Question

A spider sits on its web, undergoing simple harmonic motion with amplitude A.What fraction of each cycle does the spider spend at positions with x>0.75A? Hint: Use the analog of uniform circular motion.

Answer 1

when is sinTheta=.75?

theta=48.6deg; 131deg

so from 0 to 48.6 deg, and 131 to 180 deg, it is below A

fraction below A: (48.6+49)/180=98/180
fraction above A: 82/180

you do it more accurately.