# Lagrange equation for mass-spring-damper-pendulum

1. Aug 24, 2009

### tanquat

Can someone kind of give me a step by step as to how you get the equations of motion for this problem?

http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/images/msp.jpg

http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/msp.html
Though im not quite sure what b and c are.

i guess for reference here is what it looks like after transforming it some:
http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/msp.html

Here is the website if you need to do any clarification:
http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/msp.html

I have another problem similar to this for homework, i just wnat to see this one layed out before i work on my other. Thanks!

2. Aug 24, 2009

### kyiydnlm

$$mv_{x} + MV_{x} = C1$$

$$\int(-BV_{y})dt + \int(-KY)dt + MV_{y} + mv_{y} = C2$$

$$v_{x} = V_{x} + lsin(\varphi)\frac{d\varphi}{dt}$$

$$v_{y} = V_{y} + lcos(\varphi)\frac{d\varphi}{dt}$$

3. Aug 25, 2009

### tanquat

um, could you clarify a little bit more?
my main problem is understanding the relationship between the pendulum and the first mass, M

4. Aug 26, 2009

### kyiydnlm

uppercase symbols for M, small symbols for m.
B is damping coefficient of damper attached on M and K is spring coefficient.
apply momentum conservation on both x and y direction can get above equatiions.
C1 and C2 are initial conditions.
derivation of second equation will be force-acceleration equation.
Not difficult to understant. just "Ft + MV + mv = a constant" in differential form.
It's a second order system. If you re-arrange them, you can get simillar equations as that on the webpage you provided.
If there's something missing, might be geometry equations.

Good Luck.

Last edited: Aug 26, 2009
5. Aug 26, 2009

### tanquat

thanks i appreciate it. I just started a vibrations course and this problem is similar to what i have in homework. i tried looking tah the lagrange equations to get an idea on an answer so i can go back and do the system again using newtonian equations, though as of last night it has started making me rather frustrated :/ and honestly its the pendulum thats messing me up.