# Elliptic Pendulum: Homework on Kinetic & Potential Energies

• imjess
In summary, the conversation is about solving for the kinetic and potential energies of a uniform rod attached to a slider and constrained to move along a horizontal wire. The person is having trouble treating the rod as a continuum and is looking for advice. They have found an expression for the kinetic energy and are unsure about the x coordinate for the potential energy. They have also asked for someone to check their work.
imjess

## Homework Statement

A uniform rod AB of mass M and length 2l attatched to a slider at A which is constrained to move along a smooth horizontal wire. The rod, which is subject to gravity, is free to swing in the vertical plane containing the wire. Using Ω (the angle between rod and vertical) and x coordinate of the centre of mass, find an expression for the kinetic and potential energies, deduce Lagrange's equations. Show that the Lagrangian is regular.

## The Attempt at a Solution

I know I have to treat the rod as a continuum, but I can't get around it...

Sorry it doesn't seem like I've done much but I've tried every way I know and nothing's working, any advice would be greatly appreciated. Thank you

Could you please start me of...I know v=-2lmcosθ

But to get T could you please help me... I don't know what my x coordinate is

KE = 1/2[Mx.^2 + θ.^2 Ml^2 sin^2(θ)]

I have seemed to get this...could any1 please check if I have done this right

## 1. What is an elliptic pendulum?

An elliptic pendulum is a type of pendulum that moves in an elliptical path rather than a straight line. It is formed by suspending a weight from a fixed point with a string or rod, allowing it to swing freely.

## 2. How does an elliptic pendulum work?

An elliptic pendulum works by converting potential energy into kinetic energy and vice versa as it swings back and forth. As the weight moves towards the bottom of its path, it gains kinetic energy, and as it moves towards the top, it gains potential energy.

## 3. What is the relationship between kinetic and potential energies in an elliptic pendulum?

In an elliptic pendulum, the kinetic and potential energies are constantly changing and are inversely related. As the kinetic energy increases, the potential energy decreases, and vice versa.

## 4. How is the period of an elliptic pendulum calculated?

The period of an elliptic pendulum can be calculated using the formula T=2π√(L/g), where T is the period (time for one complete swing), L is the length of the string or rod, and g is the acceleration due to gravity.

## 5. What factors affect the motion of an elliptic pendulum?

The motion of an elliptic pendulum is affected by several factors, including the length of the string or rod, the mass of the weight, the angle of release, and the force of gravity. These factors can impact the speed, amplitude, and period of the pendulum's motion.

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