# Frequency of damped mass-spring system

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1. Mar 25, 2015

[Mentor's note: Thread title changed to reflect question content]

I really need some help with this one:

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

An unhappy rodent of mass 0.307kg , moving on the end of a spring with force constant 2.48N/m , is acted on by a damping force Fx=−b⋅vx.

Part A
If the constant b has the value 0.894kg/s , what is the frequency of oscillation of the mouse?

Part B
For what value of the constant b will the motion be critically damped?

2. Relevant equations
F = -kx
F = mg
f = 1/T = ω/2π

3. The attempt at a solution
Part A:
Fx = -bvx = -0.894⋅vx
-kx = F => m⋅a = -k⋅x, and I put the numbers in and got:
0.307⋅9.81 = -2.48⋅x => x = -1.214 m

ω = sqrt(k/m), and I put the numbers in and got: ω = 0.452 rad/s

Then I tried to calculate vx by:

vx⋅(-0.894)=3.0117 => vx = -3.369 m/s

I don't know what to do. Thankful for all help I can get!

Last edited by a moderator: Mar 25, 2015
2. Mar 25, 2015

### Avatrin

I guess the rodent is hanging from the ceiling (attached to the spring which has its other end attached to the ceiling). How far above or below equilibrium position does it start?

Also, the solutions for v(x) and F(x) are not going to be numbers (since they change with time).

Finally, if multiple forces are acting on an object F = F1 + F2 + F3. You have the gravitational force, the force from the spring and the damping force all acting on the rodent at the same time. I recommend drawing the system with all forces. It may make things easier.

3. Mar 25, 2015

### Alettix

I would start of with drawing a free body diagram, then you should be able to set up a differentialequation describing the motion of the mass.
Depending on the value of the constant b, you will be able to get different soultions to this equation, descirbing different kinds of damping. :)