# Pendulum attached to oscillating support

1. May 17, 2010

### Pollux

1. The problem statement, all variables and given/known data

The support of a pendulum has an oscillatory
vertical motion. Set up the equation of
motion for it and analyse the motion for different
values of the parameters. Will there be particular
frequences of the motion of the support that cause
particular effects? Is it for instance possible to
have the inverted position as a stable equilibrium?

this is an open-ended problem, so we can make stuff up! We are to analys the equation of motion in matlab, using ode45. We call the lenght of the string attached to the pendulum for l. The mass of the Pendulum is m, the movable support and string is massless, there is no friction.

We call the angle that the pendulum makes with the equilibrium line theta and we describe the motion of the support with Asin(phi)/2.

2. Relevant equations
L=T-V
T=(m*xdot^2+m*ydot^2)/2, V=mgy.

3. The attempt at a solution
Okey so we start out with trying to express y and x in terms of phi and theta. We got that
y=l(1-cos(theta))+(1+sin(phi))*A/2.
This will make it so that when the support is at its lowest and theta=0 then y=0.

x=lsin(theta)

This gives us the Lagrangian: