find optimal spring and damping constants using minimize in scipy

cost_function.py

def cost_function(x):

    k_spring, c_damper = x

    # import functions
    from numpy import linspace, max, abs
    from scipy.integrate import odeint
    import msd_ode
    
    # define constants
    init_cond = [0.3, -0.1]
    t_init    = 0.0
    t_final   = 100.0
    time_step = 0.005
    num_data =int((t_final-t_init)/time_step)

    # integrate 
    t_all = linspace(t_init, t_final, num_data)
    y_all = odeint(msd_ode.mass_spring_damper, init_cond, t_all, 
                   args=([k_spring, c_damper],))
    
    # find maximum undershoot               
    xout = y_all[:,0]
    x_negative = abs(xout[xout<0])
    max_undershoot = max(x_negative)
    return max_undershoot

msd_ode.py

def mass_spring_damper(state, t, k_c_set):
    x, x_dot = state
    k_spring, c_damper = k_c_set
    
    f = [x_dot,
         -k_spring*x - c_damper*x_dot] 
    return f

run_minimize.py

from scipy.optimize import minimize
import cost_function as cf

x0 = [0.1,0.1]
bnds = ((0, None), (0, None))

result = minimize(cf.cost_function, x0, method='SLSQP', bounds=bnds)

print(result.x)