Lagrange equation for massspringdamperpendulumby tanquat Tags: harmonics, lagrange, oscillations, springmass, vibrations 

#1
Aug2409, 12:52 PM

P: 3

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! 



#2
Aug2409, 04:10 PM

P: 34

[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] 



#3
Aug2509, 06:26 PM

P: 3

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



#4
Aug2609, 11:01 AM

P: 34

Lagrange equation for massspringdamperpendulum
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 forceacceleration equation. Not difficult to understant. just "Ft + MV + mv = a constant" in differential form. It's a second order system. If you rearrange them, you can get simillar equations as that on the webpage you provided. If there's something missing, might be geometry equations. Good Luck. 



#5
Aug2609, 11:14 AM

P: 3

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.



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