How to find the kinetic energy of a pendulum?

AI Thread Summary
To find the kinetic energy of a pendulum, one can use the relationship between total energy and potential energy. The total mechanical energy is determined by the height from which the pendulum is released. Kinetic energy can be calculated as the total energy minus the potential energy. The equation for kinetic energy is T = 1/2 mv², where m is mass and v is velocity. Understanding these principles allows for the calculation of kinetic energy even without direct measurements of velocity.
cytochrome
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The potential energy can be obtained with the equation

Fnet = ∇U

Where Fnet is the sum of all the forces acting on the pendulum.



How can we obtain kinetic energy when we don't know the mechanical energy or the velocity?
 
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the kinetic energy of the pendulum will be equal to the total energy minus the potential energy

the total energy of the pendulum is determined by how high up it is released
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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