# Mass Spring Damping Question

1. May 7, 2014

### rzn972

1. The problem statement, all variables and given/known data
Suppose a mass- spring is modeled by x''+ cx'+100x. What should the damping constant c be in order that critical damping occurs?

2. Relevant equations

3. The attempt at a solution
I set the discriminant equal to zero so that there are real repeated roots.
B^2-4ac=0
c^2=400.
c=20 or c=-20.
The answer should only be c=20. For critical damping, the constant must be positive?

2. May 7, 2014

### pasmith

What is the repeated root? You need it to be negative so that $x$ decays with time, do you not?

3. May 7, 2014

### AlephZero

For any level of damping, c must be positive.

If c is negative, you are putting energy into the system, not taking energy out.

4. May 7, 2014

5. May 7, 2014

### BvU

An other way to look at it: damping force must be opposite to x', which it is if c is positive:

x'' = -cx' -100x