# Ball on String, Harmonic Motion

## Homework Statement

A 2.2 kg ball is attached to a 0.638 m long string and is pulled an angle Θ from the verticle such that the center of mass of the ball is raised a distance h=0.22 m from its lowest position. The ball is released and allowed to swing down.
a) What is the angular frequency of this motion?
b) What is the period of this motion?
c) What is the velocity of the ball when the string is vertical?
d) What is the tension in the string when it is vertical?

2. The attempt at a solution

a) ω = sqrt(mgr/I) = 3.92
b) f = ω/2pi
T = 1/f = 1.603
c) I'm sure that if I could complete this I could easily find part d. I thought that I could apply conservation of energy, so I performed the following:

PEi = KEf
mgh = .5mv^2
v = sqrt(2gh)
v = sqrt(2*9.81*.22)
v = 2.0776 m/s

The software rejects this answer. I'm not sure where to go from here. Do I need to set up a differential equation to find the velocity?

Thanks!

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