Finding Length of a Pendulum from Kinetic Energy

[Dante Tufano]

Okay, so here's the question:

The figure below shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The pendulum bob has mass 0.320 kg. What is the length of the pendulum?

Equations: KE=(mv^2)/2
U=mgh
x(t)=xmcos(wt+phi)

I solved for the height by setting the max kinetic energy equal to the max potential energy, and got .004783, but I have no idea how to use the position equation to find the max velocity or what to do after that. Could I please get some guidance?

 

[The legend]

when the pendulum is in it's mean position, you know that the KE is maximum.

So, find the velocity there. Then use the conservation of energy principle assuming that that the pendulum bob rises to a height L(1-cosθ). substituting v in that equation you get

L(1-cosθ) is equal some value. You know θ when KE becomes 0 from the graph.
substitute that.

 

[Dante Tufano]

Okay, so I solve for the velocity using the max kinetic energy and have a max velocity of .3062 m/s. I set L(1-cosθ) equal to (KEmax/mg) and solved for L using the θ value .1. However, I got the wrong answer, so can I get any more clues as to what I'm doing wrong?

 

[Dante Tufano]

Sorry, I made an algebra mistake! The values came out write after I punched them in again. Thanks a lot!

 

[The legend]

oh, haha
happy to help.