Help with mass-spring modeling problem

[Aows]

Homework Statement

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 ?

Homework Equations

spring equation:
my''+cy'+ky=f(t)
consider f(t) =0

The Attempt at a Solution

stopped at first because of the first step

 

[Dr.D]

What bob? Do you have a friend named Bob?

A figure would really help, so that perhaps you would get some useful help.

 

[Aows]

you name it, anything use a mass instead. @Dr.D

 

[Mark44]

Homework Statement

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 ?

Homework Equations

spring equation:
my''+cy'+ky=f(t)
consider f(t) =0

The Attempt at a Solution

stopped at first because of the first step

The numbers in the solution you post don't make any sense to me, either. If you're sure you're looking at the right solution for this problem, another possibility is that the posted answer is wrong.

What bob? Do you have a friend named Bob?

Lead or other metal weights are often called plumb bobs, with the term "plumb" coming from the Latin plumbum (lead).

A figure would really help, so that perhaps you would get some useful help.

I think there's enough information here already, so that a drawing wouldn't be necessary. This problem seems to me to be just "fill in the blanks." From the given info, I believe the DE would be y'' + 2y' + 2y = 0, with y(0) = 4, y'(0) = 2, unless I'm missing something.

 

[Aows]

The numbers in the solution you post don't make any sense to me, either. If you're sure you're looking at the right solution for this problem, another possibility is that the posted answer is wrong.

Lead or other metal weights are often called plumb bobs, with the term "plumb" coming from the Latin plumbum (lead).
I think there's enough information here already, so that a drawing wouldn't be necessary. This problem seems to me to be just "fill in the blanks." From the given info, I believe the DE would be y'' + 2y' + 2y = 0, with y(0) = 4, y'(0) = 2, unless I'm missing something.

very helpful answer MR. @Mark44 , i also guessed that there is something wrong with the available answer, i solved it and i got completely different roots for the characteristic equation which are complex numbers (R1= 1-i, R2=1+i)

thanks indeed for your helpful answer.

 

[Dr.D]

Lead or other metal weights are often called plumb bobs, with the term "plumb" coming from the Latin plumbum (lead).

And this is relevant how? Was there some mention of lead that I missed?

I think there's enough information here already, so that a drawing wouldn't be necessary. This problem seems to me to be just "fill in the blanks." From the given info, I believe the DE would be y'' + 2y' + 2y = 0, with y(0) = 4, y'(0) = 2, unless I'm missing something.

If you are able to solve the problem without help, why are you posting? You think that there is enough information already, but I can come up with several problem geometries that fit your description and yet have different formulations. If you don't wish to fully describe the problem, don't be surprised if you get less than useful replies.

 

[Mark44]

And this is relevant how? Was there some mention of lead that I missed?

What bob? Do you have a friend named Bob?

Lead or other metal weights are often called plumb bobs, with the term "plumb" coming from the Latin plumbum (lead).

I interpreted your remark (2nd one above) to mean that you didn't understand the term "bob". I don't see that asking if the OP has a friend named Bob was at all helpful.

If you are able to solve the problem without help, why are you posting? You think that there is enough information already, but I can come up with several problem geometries that fit your description and yet have different formulations. If you don't wish to fully describe the problem, don't be surprised if you get less than useful replies.

Please reread this thread. The OP is not asking how to solve the problem, but didn't understand how the posted answer was related to the problem. As far as I can tell, the OP made a good-faith effort to provide the information in this problem, which doesn't warrant your less than helpful responses.

 

[Dr.D]

Homework Statement

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 ?

Homework Equations

spring equation:
my''+cy'+ky=f(t)
consider f(t) =0

The quote above is the original description of the problem, and the post title suggest that this is supposed to be some sort of spring-mass problem. Right away, there is some concern about just what sort of a system this is.

(1) I know the term bob (and have known it for about 70 years) in reference to a pendulum bob, but the post title speaks of a spring mass system. They are not quite the same thing. Is it a spring-mass-damper system, or is it a pendulum, or perhaps something else. A simple figure would resolve all doubt, which is why I asked for that.

(2) The problem statement speaks of the bob being "drawn upward four units." What does this mean? If this is in fact a simple pendulum, does it perhaps mean that the mass is drawn to the side to initiate the motion. No, probably not, or it would not have said "upward." Is it a hanging spring-mass system? Perhaps, and that would seem to fit the sense of upward, but we don't know that this is actually the type of system being discussed.

(3) Most folks when speaking of a mass refer to it as such. The term "bob" is used exclusively in terms of a simple pendulum as far as I am aware. The OP eventually did identify this as a mass, but it was not in the initial statement. If it is a pendulum, why not say so? If it is block hanging on a spring/damper combination, then the term "bob" is not very appropriate at all.

The main point of the questions is "where do the numbers 6 and 5 in the differential equation come from?" As the OP observed in one of his comment, it looks like a simple plug-and-chug problem, but then, the given solution does not seem to fit. What could be the matter?

(4) It may simply be a hanging spring-mass-damper system and the given ODE is simply an error from the problem source. But we have been denied a figure and don't know that, so other possibilities must be considered.

(5) There are an endless number of other kinematically complicated systems for which (a) the mass of a single (principal) mass is not the effective system mass, (b) the actual stiffness of a spring is not the effective stiffness of the system, and (c) the actual damper coefficient is not the effective system damping coefficient. When kinematics enters strongly into the situation, all bets are off on the simple answer. Could this be the reason the given ODE has unexpected coefficients? Maybe, but we are denied a sketch to show what sort of system is under consideration.

Shall we jump to the conclusion that the problem answer given is in error, or should we consider other possibilities? With no figure, no knowledge of just what sort of system is under consideration, I am reluctant to conclude that the given answer is in error.

Mark44 says, "the OP is not asking how to solve the problem." Well, from my perspective, he is asking how to resolve the discrepancy he has observed, and that may well be the same as asking how to solve the problem. If we could just have a figure, almost all of this would vanish, but without the figure (or a very clear verbal system description), we simply cannot give meaningful answers.

 

[Mark44]

The quote above is the original description of the problem, and the post title suggest that this is supposed to be some sort of spring-mass problem. Right away, there is some concern about just what sort of a system this is.

Part of our tasks here as homework helpers is to translate what a poster has written to what he or she actually means. This is not as straightforward as it might be, as many of our members are not native speakers of English. I am virtually certain that the OP falls into this category.

(1) I know the term bob (and have known it for about 70 years) in reference to a pendulum bob, but the post title speaks of a spring mass system. They are not quite the same thing. Is it a spring-mass-damper system, or is it a pendulum, or perhaps something else. A simple figure would resolve all doubt, which is why I asked for that.

You are being overly pedantic. As you note below, there was no mention of a pendulum. Further, one can reasonably infer from the equations shown that the system is indeed a damped spring-mass system with a given initial position and initial velocity.

(2) The problem statement speaks of the bob being "drawn upward four units." What does this mean? If this is in fact a simple pendulum, does it perhaps mean that the mass is drawn to the side to initiate the motion. No, probably not, or it would not have said "upward." Is it a hanging spring-mass system? Perhaps, and that would seem to fit the sense of upward, but we don't know that this is actually the type of system being discussed.

But to assume that the OP really meant a pendulum system is something of a stretch, given that there was no mention whatsoever of this.

(3) Most folks when speaking of a mass refer to it as such. The term "bob" is used exclusively in terms of a simple pendulum as far as I am aware. The OP eventually did identify this as a mass, but it was not in the initial statement. If it is a pendulum, why not say so? If it is block hanging on a spring/damper combination, then the term "bob" is not very appropriate at all.

Again, you are being overly pedantic, IMO, especially in assuming that all members of this site are equally fluent in English.

The main point of the questions is "where do the numbers 6 and 5 in the differential equation come from?" As the OP observed in one of his comment, it looks like a simple plug-and-chug problem, but then, the given solution does not seem to fit. What could be the matter?

(4) It may simply be a hanging spring-mass-damper system and the given ODE is simply an error from the problem source. But we have been denied a figure and don't know that, so other possibilities must be considered.

It is not rare for answers in textbooks, especially those in post-calculus courses to have errors in the answers. Since you have been aware of the meaning of "bob" for 70 years, I suspect that you know this as well as I do.

(5) There are an endless number of other kinematically complicated systems for which (a) the mass of a single (principal) mass is not the effective system mass, (b) the actual stiffness of a spring is not the effective stiffness of the system, and (c) the actual damper coefficient is not the effective system damping coefficient. When kinematics enters strongly into the situation, all bets are off on the simple answer. Could this be the reason the given ODE has unexpected coefficients? Maybe, but we are denied a sketch to show what sort of system is under consideration.

The principle of Ockham's Razor comes to mind here -- if there are two or more explanations to some situation, start by first looking at the simplest, which in this case would be a damped mass-spring system as described in the first post..

Shall we jump to the conclusion that the problem answer given is in error, or should we consider other possibilities? With no figure, no knowledge of just what sort of system is under consideration, I am reluctant to conclude that the given answer is in error.

Mark44 says, "the OP is not asking how to solve the problem." Well, from my perspective, he is asking how to resolve the discrepancy he has observed, and that may well be the same as asking how to solve the problem. If we could just have a figure, almost all of this would vanish, but without the figure (or a very clear verbal system description), we simply cannot give meaningful answers.

A figure would be nice, but if we assume, as I have done, that this is a straightforward damped mass-spring system, we can make conjectures.

Since the OP has marked this problem as solved, I am also closing this thread. If the OP believes that there is more to be said, I will leave it to him/her to send me a PM to that effect.

 

[Aows]

Thanks all for your useful contributions,
Mr. @Mark44 explains everything in a smooth and clear way.
regarding the figure, the problem that I have doesn't has any figure with it, and IMHO, there is no need to figure for this problem.
i marked the problem as solved because I asked many in other forum which all agreed that there is a mistake in the solution or in the original numbers of the problem which as Mr. @Mark44 mentions this occurred a lot in many textbooks.
thanks again everyone and to Mr. @Mark44 for the useful contribution,

Regards,
Aows K.