# Damped Oscillation

1. Jan 29, 2008

### razor108

1. The problem statement, all variables and given/known data
A damped oscillator of mass m=1,6 kg and spring constant s=20N/m has a damped frequency of \omega' that is 99% of the undamped frequency \omega.

As found out by me:
The damping constant b is 0.796 kg/s.
Q of the system is 7.1066 kg^-1.
Are the units here right?

The questions are:
a) Confirm that the system is lightly damped.
b) What new damping constant b_new is required to make the system critically damped?
c) Using b_new calculate the displacement of the mass at t=1,0s given that the displacement is zero and the velocity is 5,0 m/s at t=0.

2. Relevant equations
To calculate b I used
\omega' = ( \omega^2 - b/2m)^1/2

To calculate Q I used
Q = ((mass*spring constant)^1/2)/b

3. The attempt at a solution

I couldn't find any specific definition of when a system is lightly damped.
I found somewhere that if \omega' is about equal to \omega the system is lightly damped, which is the case here (\omega' = 99%\omega) but this can't be the answer since I have to find a new damping constant.

If I had the new damping constant I would just use the given data to make up a wave equation for x(t).

Thanks for helping.

2. Jan 31, 2008

### hage567

I think this should be $$\omega' = \sqrt{\omega^2 - (\frac{b}{2m})^2}$$

I think lightly damped means the same and underdamped. It just means the system is not critically damped or overdamped. So it is just damped enough that the amplitude decreases exponentially over time but still oscillates.

But in that part of the question you are supposed to find the new damping constant that would make the system critcally damped, that's a different situation.

Hope that helps.