Find Pendulum Length from Kinetic Energy & Angle Graph

[pingpong240]

Homework Statement

The figure below shows the kinetic energy K of a simple pendulum versus its angle θ from the vertical. The pendulum bob has mass 0.260 kg. What is the length of the pendulum?

Homework Equations

K=(1/2)mv²
U=mgh
x(t)=x_m*cos(w*t+phi)

*where w is the angular frequency, and the wt + phi being the phase

The Attempt at a Solution

Basically I have gone through a series of approaches to this problem, but I have come to settle with this one:

I started by getting phi from the graph, .100 radians. Then, I attempted to relate gravitational potential energy to the max kinetic energy that was given from the graph (.015 J). This way, I could get h, and relate h to the maximum angle and the pendulum length. To do that, I would use x(t)=x_m*cos(w*t+phi). I'm not sure if I should use the simple pendulum equations, but I don't think I need to know the inertia.

 

[rl.bhat]

x(t)=xm*cos(w*t+phi)
From the above equation find the maximum velocity x(t)=xm*cos(w*t+phi)m.
KE is given. Mass is given. Find the value of Vm.
Since angular displacement is only 0.1 rad, it is SHM.
In SHM f = -kx, ...(1)
In simple pendulum, restoring force = -mg(theta) = -mgx/L...(2)
From eq. 1 and 2. find the value of k = mg/L ...(3)
From 3 find the value of omega. And proceed.

 

[pingpong240]

Thanks for the help. : ) I computed the answer to be 1.177 m. This checked out. I understand the methodology behind it too, thanks again.