# Short Change Resonance of a Damped, driven oscillator

1. Apr 19, 2013

### bd2015

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

If both k of the spring and m are doubled while the damping constant b and driving force magnitude F0 are kept unchanged, what happens to the curve, which shows average power P(ω)?

Does the curve:
a) The curve becomes narrower (smaller ω) at the same frequency;
b) The curve becomes narrower at a higher frequency;
c) The curve becomes broader (larger ω) at the same frequency
d) The curve becomes broader at a different frequency;
e) The curve does not change;

3. The attempt at a solution
Equation of motion is:
m$\frac{d2x}{dt2}$+b$\frac{dx}{dt}$+kx=FoCos(ωt)

Conceptually, it seems that the amount of power would not necessarily change of k is doubled as is the mass. It also seems that since k/m = ω^2, Δω shouldn't change. Not sure if this is correct.

Last edited: Apr 19, 2013
2. Apr 19, 2013

### TSny

There's a typographical error in the first term of your equation of motion. After fixing that, divide the equation through by the mass m. Examine the coefficients of each term and determine how the formula for average power would be modified if m and k are doubled.