Lagrange equation for mass-spring-damper-pendulum

AI Thread Summary
The discussion focuses on deriving the equations of motion for a mass-spring-damper-pendulum system using the Lagrange equation. Key points include the need for clarification on variables such as b (damping coefficient) and c (spring coefficient), as well as the relationship between the pendulum and the masses involved. Participants emphasize applying momentum conservation in both x and y directions to formulate the equations. The conversation also highlights that the problem is a second-order system and suggests that geometry equations might be necessary for a complete understanding. Overall, the discussion aims to clarify the complexities of the system for better comprehension and application in related homework problems.
tanquat
Messages
3
Reaction score
0
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

the answer is this:
http://www.enm.bris.ac.uk/teaching/projects/2002_03/ca9213/msp.html
Though I am 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!
 
Engineering news on Phys.org
<br /> <br /> mv_{x} + MV_{x} = C1<br /> <br />

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

<br /> <br /> v_{x} = V_{x} + lsin(\varphi)\frac{d\varphi}{dt}<br /> <br />

<br /> <br /> v_{y} = V_{y} + lcos(\varphi)\frac{d\varphi}{dt}<br /> <br />
 
um, could you clarify a little bit more?
my main problem is understanding the relationship between the pendulum and the first mass, M
 
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:
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 that's messing me up.
 
I need some assistance with calculating hp requirements for moving a load. - The 4000lb load is resting on ball bearing rails so friction is effectively zero and will be covered by my added power contingencies. Load: 4000lbs Distance to travel: 10 meters. Time to Travel: 7.5 seconds Need to accelerate the load from a stop to a nominal speed then decelerate coming to a stop. My power delivery method will be a gearmotor driving a gear rack. - I suspect the pinion gear to be about 3-4in in...
How did you find PF?: Via Google search Hi, I have a vessel I 3D printed to investigate single bubble rise. The vessel has a 4 mm gap separated by acrylic panels. This is essentially my viewing chamber where I can record the bubble motion. The vessel is open to atmosphere. The bubble generation mechanism is composed of a syringe pump and glass capillary tube (Internal Diameter of 0.45 mm). I connect a 1/4” air line hose from the syringe to the capillary The bubble is formed at the tip...
Thread 'Turbocharging carbureted petrol 2 stroke engines'
Hi everyone, online I ve seen some images about 2 stroke carbureted turbo (motorcycle derivation engine). Now.. In the past in this forum some members spoke about turbocharging 2 stroke but not in sufficient detail. The intake and the exhaust are open at the same time and there are no valves like a 4 stroke. But if you search online you can find carbureted 2stroke turbo sled or the Am6 turbo. The question is: Is really possible turbocharge a 2 stroke carburated(NOT EFI)petrol engine and...
Back
Top