## gerryliyana 2 years ago How many number of degrees of freedom of these system??

1. gerryliyana

2. guyofreckoning2

can you provide a higher quality?

3. gerryliyana

what do you mean?

4. guyofreckoning2

I cannot understand the picture... it's too difficult too read

5. guyofreckoning2

*to

6. guyofreckoning2

wait nvm

7. guyofreckoning2

6's? are they 6's in the partial circles?

8. gerryliyana

itsn't 6

9. guyofreckoning2

I am sorry to admit I cannot, I probably just provided false hope and nothing else, I thought it were a pic of something else but I was wrong, not too good at that.. Sorry, I am truly sorry. It's running slow tonight and everything.

10. guyofreckoning2

but at least I can provide a medal

11. gerryliyana

ok no problem ..., :)

12. guyofreckoning2

heh, the place is running slow tonight, kinda mean to drop in and not answer someone's question

13. kr7210

its a coupled oscillator and its degree of freedom is "one"

14. kr7210

2*2-1-1-1=1

15. Vincent-Lyon.Fr

There are two degrees of freedom.

16. gerryliyana

why??

17. aero_elastic

Assuming the two rods that the masses are suspended from are fixed (their length won't change) there is two degrees of freedom in the system. The position of each rod can be written in terms of its angular displacement (1DOF each). The length of the spring too can be written in terms of the two theta terms (assuming one knows the distance between base of the two rods that the masses are suspended from). The system can be described in more terms (x,y coordinates of masses 1&2), but two are all that's needed.

18. gerryliyana

ok, i saw when n independent coordinates are required to specify the position of the masses of a system, the system is of n degrees of freedom. For example if the masses m1 and m2 are contrained to move vertically, at least one coordinate (just call x(t)) is required to define the location of each mass at any time. Thus te system requires altogether two coordinates to specify their positions; it is a two-degree-of-freedom system.., right???

19. Vincent-Lyon.Fr

You're right.

20. Vincent-Lyon.Fr

Is it just a question about degrees of freedom or do you have to derive the equations of motion of this system?

21. gerryliyana

very nice.., thank u @Vincent-Lyon.Fr . it isn't only a question about degrees of freedom, i do have to derive the equations of motion, but in coupled oscillations of a loaded string

22. gerryliyana

until to obtain wave equation

23. gerryliyana

follow me: I finally did read a book "The Physics of Vibrations and Waves) by HJ Pain. It show how the coupled vibrations in the periodic structur of the loaded string become waves in a continuous medium. The equations of motion of the r-th mass to be: $\frac{ d^{2}y_{r} }{ dt^{2} } = \frac{ T }{ma } (y_{r+1} - 2y_{r} + y_{r-1})$ then separation a = dx and consider the limit dx --> 0 as the masses merge into a continuous heavy string. The: $\frac{ d^{2}y_{r} }{ dt^{2} } = \frac{ T }{ m } \left( \frac{ y_{r+1}-2y_{r} + y_{r-1} }{ dx} \right) = \frac{ T }{ m }\left( \frac{ (y_{r+1} - y_{r}) }{ dx } -\frac{ (y_{r}-y_{r-1}) }{ dx } \right)$ $= \frac{ T }{ m } \left[ \left( \frac{ dy }{ dx } \right)_{r+1} - \left( \frac{ dy }{ dx } \right)_{r} \right]$ and $\left( \frac{ dy }{ dx } \right)_{x+dx} - \left( \frac{ dy }{ dx } \right)_{x} =\frac{ d^{2}y }{ dx^{2} } dx$ I'm a little bit confused by: $\left( \frac{ dy }{ dx } \right)_{x+dx} - \left( \frac{ dy }{ dx } \right)_{x} =\frac{ d^{2}y }{ dx^{2} } dx$ why $$\left( \frac{ dy }{ dx } \right)_{x+dx} - \left( \frac{ dy }{ dx } \right)_{x}$$ is equal to $$\frac{ d^{2}y }{ dx^{2} } dx$$ ?????

24. Aperogalics

@gerryliyana it is simple just think practically let dy/dx=t then if i divide it by dx i.e. |dw:1355218737331:dw| then it is derivative :)

25. gerryliyana

what if it's second derivative???

26. Aperogalics

means???????

27. gerryliyana

If dy/dx = t shown by $\frac{ t_{m+dm}-t_{m} }{ dm }$ how the form formula for second derivative?

28. Aperogalics

it would be |dw:1355219544429:dw| but t=dy/dm so |dw:1355219573174:dw|

29. Aperogalics

@gerryliyana

30. gerryliyana

|dw:1355219655154:dw|

31. Aperogalics

If dy/dx = t shown by tm+dm−tm/dm how the form formula for second derivative? in ur post @gerryliyana can you tell from where dm comes??????????

32. gerryliyana

ok ok i got it.., i'm sorry ..., hehe

33. Aperogalics

no prob. :)

34. gerryliyana

Ok, so $y' = \lim_{dx \rightarrow 0} \frac{ y_{x+dx} - y_{x} }{ dx }$ and for second derivative $y'' = \lim_{dx \rightarrow 0} \frac{ y'_{x+dx} - y'_{x} }{ dx }$ $dx y''= y'_{x+dx} - y'_{x}$ $dx \frac{ d^{2}y }{ dt^{2} } = \left( \frac{ dy }{ dx } \right)_{x+dx} - \left( \frac{ dy }{ dx } \right) _{x}$ Ok??????

35. kr7210

i'm sorry, a coupled oscillator have 2 degree of freedom coz of have two generalized coordinate to describe the system, sorry again.

36. gerryliyana

ok no problem @kr7210 thank you for coming :)

37. Aperogalics

@gerryliyana it's correct now :)