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gerryliyana
How many number of degrees of freedom of these system??
can you provide a higher quality?
I cannot understand the picture... it's too difficult too read
6's? are they 6's in the partial circles?
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.
but at least I can provide a medal
ok no problem ..., :)
heh, the place is running slow tonight, kinda mean to drop in and not answer someone's question
its a coupled oscillator and its degree of freedom is "one"
There are two degrees of freedom.
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.
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???
Is it just a question about degrees of freedom or do you have to derive the equations of motion of this system?
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
until to obtain wave equation
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 \(\frac{ d^{2}y }{ dx^{2} } dx\) ?????
@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 :)
what if it's second derivative???
If dy/dx = t shown by \[\frac{ t_{m+dm}-t_{m} }{ dm } \] how the form formula for second derivative?
it would be |dw:1355219544429:dw| but t=dy/dm so |dw:1355219573174:dw|
|dw:1355219655154:dw|
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??????????
ok ok i got it.., i'm sorry ..., hehe
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??????
i'm sorry, a coupled oscillator have 2 degree of freedom coz of have two generalized coordinate to describe the system, sorry again.
ok no problem @kr7210 thank you for coming :)
@gerryliyana it's correct now :)