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Dynamics help please

The energy for a pendulum and masses is given by:
E = 1/2L 2θ˙ 2(m 1 + 4m 2) − Lg(m 1 + 2m 2) cos θ + E0

With eo a constant. How do you use conservation of energy to find the equation of motion for theta?

Reply 1

atsruser

Original post by Harriettttttt1

The energy for a pendulum and masses is given by:
E = 1/2L 2θ˙ 2(m 1 + 4m 2) − Lg(m 1 + 2m 2) cos θ + E0

This is unreadable. Can you put it up in latex, or post a copy of the question, please?

With eo a constant. How do you use conservation of energy to find the equation of motion for theta?

In general, you differentiate it e.g. consider conservation of motion for a body falling under gravity; its energy, E, is constant:

E = \frac{1}{2}mv^2 +mgh

Differentiate this w.r.t

t

to get:

0 = mv\dot{v} +mg\frac{dh}{dt} = mv\dot{v} +mgv \Rightarrow m\dot{v} = -mg

i.e. mass x acceleration = force

This can be generalised to any case where you have a conservative force acting (i.e. a force like gravity, not like friction).