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Old Aug 30th 2017, 09:09 AM   #1
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mass-spring prpblem

the problem:
Suppose at time zero, the bob was drawn upward four units from the equilibrium position, let C=2, K=2, m=1 lbm, initial speed=2 unit/sec find an expression for body's position.

and in the solution it says: y''+6y'+5y=0
my question is: from where does the numbers (6) and (5) that is in te above DE came from ?

2. Relevant equations
spring equation:
my''+cy'+ky=f(t)
consider f(t) =0

3. The attempt at a solution
stopped at first because of the first step

Last edited by aows61; Aug 30th 2017 at 01:31 PM. Reason: correction
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Old Aug 30th 2017, 12:25 PM   #2
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Have you got some kind of friction in the problem? A spring ODE doesn't usually have a velocity term unless some kind of dampening is involved.
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Old Aug 30th 2017, 12:28 PM   #3
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spring-mass

Originally Posted by kiwiheretic View Post
Have you got some kind of friction in the problem? A spring ODE doesn't usually have a velocity term unless some kind of dampening is involved.
this is all the information that i have about the problem:
and here is a link of you want to check:
>>>https://i.imgur.com/xjqAOUY.jpg
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Old Aug 30th 2017, 01:18 PM   #4
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Originally Posted by aows61 View Post
this is all the information that i have about the problem:
and here is a link of you want to check:
>>>https://i.imgur.com/xjqAOUY.jpg
Can't see your link, why can't you attach it here?

y' is the velocity and you say that at t=0 the velocity = +2.

This is a differential equation you can solve for the boundary condition.

But what I don't know is what your sign convention is.

Which way is + and which way is -?
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Old Aug 30th 2017, 01:29 PM   #5
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here is the attachment, just press on this link>>>>> https://imgur.com/xjqAOUY
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Old Aug 30th 2017, 01:30 PM   #6
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for the sign convention:
upward is negative
and downward is positive
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Old Aug 30th 2017, 01:32 PM   #7
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I think he meant like this (reattached)
Attached Thumbnails
mass-spring prpblem-xjqaouy.jpg  
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Old Aug 30th 2017, 01:33 PM   #8
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THanks indeed @KIWIHERETIC ,
appreciate your help,
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Old Aug 30th 2017, 01:46 PM   #9
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I think the issue is either (a) the answer is incorrect in that it doesn't agree with the values of c and k that are given, or (b) there are units at play here that have not been properly defined. For example, they say m = 1 lb_m, so the first term of the DE must be divided by 32.2 lbm-ft/lbf-s^2 in order to get units of force in lbf for a given acceleration in ft/s^2. Unfortunately we are not told what the units of c and k are. If we assume that c is in lbf/(ft/s) and k is in lbf/ft, then the DE would be:

$\displaystyle \frac 1 {32.2} y'' + 2 y' +2y = 0$

But the problem states that the initial displacement is "4 units," not 4 ft, and initial velocity is "2 units per second," not 2 ft per second, so I'm guessing that somewhere in the original problem statement they define what they mean by a distance of 1 "unit." They should also be clear about what the units are for both C and K.
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Last edited by ChipB; Aug 30th 2017 at 02:14 PM.
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Old Aug 30th 2017, 01:54 PM   #10
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thanks

Originally Posted by ChipB View Post
I think the issue is either (a) the answer is incorrect in that it doesn't agree with the values of c and k that are given, or (b) there are units at play here that have not been properly defined. For example, they say m = 1 lb_m, so the first term of the DE must be divided by 32.2 lbm-ft/lbf-s^2 in order to get units of force in lbf for a given acceleration in ft/s^2. Unfortunately we are not told what the units of c and k are. If we assume that c is in lbf/(ft/s) and k is in lbf/ft, then the DE would be:

$\displaystyle \frac 1 {32.2} y'' + 2 y' +2y = 0$

But the problem states that the initial displacement is "4 units," not 4 ft, and initial velocity is "2 units per second," not 2 ft per second, so I'm guessing that somewhere in the original problem statement there were units defined for m, c and k that we don't know about.
thanks indeed for your contributions,
i also guess that there is some mistake within the solution.
even though there is some unit change it will not produce any 5 or 6, right ?
i solved it and the roots of the characteristic equation were complex (r1=-1-i, and r2=-1+i)
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