Is Energy Conserved in Pendulum Motion?

AI Thread Summary
In pendulum motion, the sum of kinetic and potential energy remains constant throughout the swing, demonstrating energy conservation. The kinetic energy is dependent on the angular velocity, while potential energy is related to the height of the pendulum. The Hamiltonian, representing total energy, does not change over time, confirming that energy is conserved. It is essential to assume that gravitational force is conservative and that tension does no work on the system. Understanding these principles clarifies the energy dynamics in pendulum motion.
maracxos
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Hello!
I need to solve this problem
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish
 
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Is this for homework? What have you tried so far?
 
no it is not for homework i had that question on exam and i didnt know the answer and i have thinked and thinked after that abaut that and i don't know the solution I have tried to solve that problem with trigonometry but nothing after that i try to solve energy for some dot A on the swing and for some dot B on the swing but my results for dot A and B are not the same...
 
maracxos said:
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish

If you describe the motion of the pendulum by the angle, say theta, and the write down the kinetic energy T and the potential energy V you will see that T is quadratic in the time derivative of theta and V is only a function of position theta.
In such a system the Hamiltonian H will be the total energy H = T + V = E and since H does not depend explicitly on time the partial derivative of H with respect to time is zero and hence H is conserved during the motion of the system.
 
Welcome to PF!

maracxos said:
Hello!
I need to solve this problem
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish

Hi maracxos! Welcome to PF! :smile:

What are you allowed to assume?

Can you assume that gravitational force is conservative?

If so, then just prove that there is no work done by the only other external force … the tension. :smile:
 
Ok thank you!
 

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