42.sagews

import scipy.integrate
import numpy as N
from sage.ext.fast_eval import fast_float
y,yp,t=var("y,yp,t")

In the interact below, the black line represents the forcing function and the blue line represents $u(t)$, which gives the position of the mass.

@interact
def plot_de(
#mgk = input_grid(1,3,default=[1,0.125,1],label="m,g,k",width=10),
initial = input_grid(1,2,default=[0,0],label="u(0), u'(0)",width=10),
m = slider(1,10),g=(0,10),k=(1,10),
forcing=input_box(3*cos(2*t),type=SR),
#max_t=slider(0,100,default=10),
#num_points = slider(100,1000,default=500)
):
#    m,g,k = mgk[0]
    max_t = 40
    num_points=500
    xmin,xmax = 0,max_t
    u0, u0p = initial[0]
    fast_deriv = fast_float(-g/m*yp-k/m*y+forcing(t), "y","yp","t")
    def f(Y,t):
        y,yp = Y
        return yp, fast_deriv(y,yp,t)
    points = N.linspace(float(xmin),xmax,num_points)
    lp = list_plot(zip(points,[i[0] for i in scipy.integrate.odeint(f,[u0,u0p],points)]), plotjoined=True,thickness=2)
    force=plot(forcing,(t,xmin,xmax),rgbcolor=(0,0,0), thickness=0.5)
    show(lp+force)

u(0), u'(0)  m  g  k  forcing  [removed] [removed] [removed] [removed]