# Lagrange Function for a certain problem

## Homework Statement

A particle of mass m is connected by a massless spring of force constant k and unstressed
length r0 to a point P that is moving along a horizontal circular path of radius a at a
uniform angular velocity ω. Verify the Lagrange-Function!

## Homework Equations

Could there be a typing error in the book (the book provided the solution which can be seen in the file "function.png". My own solution just differs in the term with r and has 1/2*m*r^2*theta' instead of 1/2*m*r*theta' like shown in the book. However i think my solution is right or can anybody find a mistake?

## The Attempt at a Solution

x(t):=a*cos(omega*t)#this is the x-coordinate of P
y(t):=a*sin(omega*t)#this is the y-coordinate of P
x(t):=x(t)+r(t)*cos(theta(t))#this is the x-coordinate of m
y(t):=y(t)+r(t)*sin(theta(t))#this is the y-coordinate of m
T := (1/2)*m*((diff(x(t), t))^2+(diff(y(t), t))^2)
V :=(1/2)*k*(r-r)^2
L=T-V

I attached a drawing of the exercise and two lagrange functions (from the book and my solution) and a Maple file for convenience.

## The Attempt at a Solution

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