Question

a swinging pendulum eventually comes to rest is this violation of law of conservation of energy

Answer 1

Question 20944

A swinging pendulum eventually comes to rest. Is this violation of law of conservation of energy?

No, it is not. Total energy of pendulum is dissipated through friction of pendulum with air (or other substance).

In ideal variant of pendulum (where we ignore the friction), the one-dimensional solution is $x = A\cos (wt + a)$ , and corresponding energy is $E = m\frac{\dot{x}^2}{2} + \frac{kx^2}{2} = \frac{mw^2a^2}{2}$ , and it doesn't change with time (the pendulum swings for infinitely long time).

But, pendulum with friction has a solution $x = Ae^{-k t}\cos (wt + a)$ , and it comes to rest with time. Total energy is then a function of time, and it goes to zero for high times. Approximately, the picture for total energy looks like this: