Normal modes: Spring and pendulum

AI Thread Summary
The discussion centers on a disagreement regarding the kinetic energy expression for a mass in a spring-pendulum system. The participant believes the provided solution for kinetic energy, denoted as T2, is incorrect and presents their own formulation. They express uncertainty about their reasoning but assert that their version of T2 appears accurate. Additionally, they suggest that the expression can be simplified for small oscillations. The overall consensus is that the original solution for T2 needs revision.
LCSphysicist
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I was doing the exercise as follows:
oi.png

I am not sure if you agree with me, but i disagree with the solution given.
I was expecting that the kinect energy of the mass ##m## (##T_2##) should be $$T_2 = \frac{m((\dot q+lcos(\theta)\dot \theta)^2 + (lsin(\theta) \dot \theta)^2)}{2}$$
I could be wrong, of course, but i have tried to figure out my error and was not able to discover. So my guess is that the solution can be wrong.
 
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Your expression for ##T_2## looks correct. For small oscillations it can be simplified a little.

The expression for ##T_2## in the solutions is not correct.
 
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