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In TBR they tell you that the kinetic energy will equal the potential energy in a pendulum system at 1/8th of a period.

There is also a question:

There is also a question:

*19. At what point in the cycle of a pendulum does the kinetic energy equal the potential energy?*

A.t=0

B. t= pi/2

C. t= (3pi)/4

D. t=(3pi)/2

A.t=0

B. t= pi/2

C. t= (3pi)/4

D. t=(3pi)/2

**Choice C is the best answer**. At t = 0, the system is motionless, so it has KE = 0 and PE at a maximum. This eliminates choice A. At pi/2 the bob is at its lowest point, moving left. At 3pi/2 the bob is at its lowest point, moving right In both cases, KE is maximum and PE is minimum. Because the pendulum has the same energetics at pi/2 as it has at 3pi/2, choices B and D are eliminated. Choice C is the best answer, because it is the only remaining answer. At 3pi/4 the bob is half way between its lowest point and highest point, moving left This falls half way between points where KE is maximum and PE is maximum. The best answer is choice C.**I am having a hard time understanding this question and the idea the KE = PE at 1/8th period. Can someone please explain both conceptually and mathematically?**
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