Lagrange equation for mass-spring-damper-pendulum

tanquat

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



the answer is this:

Though im not quite sure what b and c are.

i guess for reference here is what it looks like after transforming it some:


Here is the website if you need to do any clarification:
http://www.enm.bris.ac.uk/teaching/p...a9213/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!

kyiydnlm

[tex]

mv_{x} + MV_{x} = C1

[/tex]

[tex]

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

[/tex]

[tex]

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

[/tex]

[tex]

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

[/tex]

tanquat

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

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.

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.