Help in logic for amplitude vs frequency

[ChrisVer]

I am trying to solve the problem 4.8 found http://phys.csuchico.edu/ayars/312/Handouts/comp-phys-python.pdf at pdf's page 115-6 [book's page 107-8].

My code so far is:

from mytools import rungekuta4
from pylab import *

#set globals
G=9.81
MASS=1.0
K=42.0
MU=0.15
A=1.
OMEGA=0.01

#set diff solver variables
N=1000
tau=5.
dt= tau/float(N-1)
t=linspace(0,tau,N)

def Fexternal(A,w,t):
    return A*cos(w*t)

def springmass(xv_vector,time):
    # x' =v
    # v' = -k/m x +/- mu g + F[t]
    diff0= xv_vector[1]
    if diff0>0:
        diff1= -(K/MASS)*xv_vector[0] - MU*G +  F(A,OMEGA,time) / MASS
    else:
        diff1= -(K/MASS)*xv_vector[0] + MU*G + F(A,OMEGA,time) / MASS

    return array([diff0,diff1])

xo=1.0
vo=0.0

y=zeros([N,2])
y[0,0]=xo
y[0,1]=vo

for i in range(N-1):
     y[i+1]= rungekuta4(y[i],t[i],dt,springmass)

plot(t,y[:,0],'r-')
show()

My problem is that I cannot see how I can make the w a variable... So that I could plot the amplitude vs the omega...

 

[BvU]

Yes, it's a bit weird they ask this in a chapter where most of the material is about integrating differential equations. I think here you really need the expressions for the damped driven harmonic oscillator