Mechanical Motion of Springs Differential Equations

[TranscendArcu]

Homework Statement

The Attempt at a Solution

So I've been interpreting the information in the problem as follows: F_{damping} = 4u' = μ(u'), k = \frac{4N}{m}. If the system is critically damped then μ = 2\sqrt{km} = 2\sqrt{\frac{4N}{m}m} = 2\sqrt{4N}. Now it seems as though the spring constant is cancelling out my mass, so if μ =4 then simply force N =1 and the system is critically damped for any mass. But then, this doesn't seem quite right. I must be misunderstanding the problem.

 

[HallsofIvy]

The "m" in N/m is NOT the mass. Nor is N a parameter. That is just saying that the spring constant is 4 Newtons per meter.

 

[TranscendArcu]

Let me see if I can do better with this now. I write,

Critically damped implies μ = 2\sqrt{km}. Given that F_{damping} = μ(u') = 4u', then μ = 4 and we then say 4 = 2\sqrt{4m} which implies that m = 1.