# 2-DOF problem with unknown stiffness and velocity

## Homework Statement

I have a 2-DOF system, whereby I have one body that is grounded by a spring (body A), and a second body (body B) attached to the first by a spring and a viscous damper. For body A, I know the velocity and amplitude (before body B is added). I think I also have the stiffness value for body A (I'm looking at some old notes and I think this was given as part of the original problem). For body B, I know the mass and the damping coefficient.

I would like to solve the velocity or stiffness of body B (by knowing one I can solve the other). With the information I have, is this possible, or must one of these values be known to begin with?

## Homework Equations

equation of motion for body A:
MAx"A+KAxA+KB(xA-xB)+c(x'A-x'B)=P0sinωt

body B:
MB+x"B+KB(xB-xA)+c(x'B-x'A)=0

## The Attempt at a Solution

I've attempted to rearrange the equation above, but ultimately I think I have 2 unknowns here, the velocity and stiffness of B, and I'm uncertain if it is possible to calculate these values without firstly knowing the other. I have Den Hartog's Mechanical Vibrations book which has an example of such a system, but it assumes that these values are already known.

I have all the above information in my notes, so I have been able to check my attempts against the real values, but I am certain that in this problem I did not have stiffness/velocity for B to begin with.

Any assistance would be greatly appreciated, I am quite new to this area of study so please don't hold back if I have made any glaring errors or I'm missing anything obvious!

Thanks,

Nigel