# Homework Help: Mechanical Motion of Springs Differential Equations

1. Apr 23, 2012

### TranscendArcu

1. The problem statement, all variables and given/known data

3. 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.

2. Apr 23, 2012

### 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.

3. Apr 23, 2012

### 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.