i think ive got it

scripts/string_model_ss.py

@@ -30,22 +30,23 @@ import math
 # where A = diagonal matrix of A_n and B = [ 0 b_1 0 b_2 ... b_n]^T
 
 # lets start with 3 nodes where the string is tuned to 440hz (we'll get to arbitrary modes evantually)
-f_1 = 440 # fundamental frequency
+f_1 = 100 # fundamental frequency
 def f_n(n):
     return f_1 * n
-omega_1 = 2*math.pi*f_1
-b = 0.01
+omega_0 = 2*math.pi*f_1
+b = 1.5
+c = 2
 def omega_n(n):
     # return 2*math.pi*f_n(n) # a cooler option would be omega_n = c*n*omega_1*sqrt(1+B*n^2) to factor in string stiffness to its vibration mode
-    return 1.001*omega_1*math.sqrt(1+b*n**2)
+    return c*n*omega_0*math.sqrt(1+b*(n-1)**2)
 
 # x = [ q1, q1dot, q2, q2dot, q3, q3dot ]^T < --state vector
 omega_1 = omega_n(1)
 omega_2 = omega_n(2)
 omega_3 = omega_n(3)
-zeta_1 = 0.0001 # i guessed
-zeta_2 = 2 * zeta_1
-zeta_3 = 3 * zeta_1
+zeta_1 = 0.001 # i guessed
+zeta_2 = 1.5 * zeta_1
+zeta_3 = 2 * zeta_1
 A = [
         [          0,                 1,           0,                 0,           0,                 0],
         [-omega_1**2, -2*zeta_1*omega_1,           0,                 0,           0,                 0],
@@ -56,7 +57,7 @@ A = [
     ] # isnt this formatting gorgeous
 
 B = [ [0], [0.707], [0], [0], [0], [-0.707] ]
-c_1 = 0.0001
+c_1 = 0.002
 c_2 = c_1 / 2
 c_3 = c_1 / 3
 C = [[-c_1*omega_1**2, -2*c_1*zeta_1*omega_1, -c_2*omega_2**2, -2*c_2*zeta_2*omega_2, -c_3*omega_3**2, -2*c_3*zeta_3*omega_3]]
@@ -77,6 +78,11 @@ sys = sig.StateSpace(A, B, C, D)
 # step Response
 t, y = sig.impulse(sys, T=t)
 
+for i in range(t.size):
+    y[i] = math.tanh(y[i])/2
+    if(y[i] > 1):
+        print("what", y[i])
+
 # plotting
 plt.plot(t, y)
 plt.title("Step Response")