1
$\begingroup$

How can one calculate the amount of energy needed to displace pendulum with given mass m and string length L to $\alpha$ degrees from resting position when acceleration due to gravity is known?

$\endgroup$
1
$\begingroup$

By considering the variation in the potential energy $V=mg\Delta y$ due to the vertical displacement $\Delta y$.

A displacement of an angle $\alpha$ would move the mass of the pendulum horizontally by $\Delta x=L \sin\alpha$ and vertically by $\Delta y=L(1- \cos\alpha)$.

Therefore the energy required for a displacement of an angle $\alpha$ amounts to $mgL( 1-\cos\alpha)$.

If the pendulum is a bar or more generally an object of any shape, of course, you replace L by the distance from the pivot to the centre of mass.

$\endgroup$
  • $\begingroup$ Here $ g$ is the gravitational acceleration $\endgroup$ – Semola Jul 8 '14 at 14:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.