diff --git a/ME_2046/HW4/S25HW4.pdf b/ME_2046/HW4/S25HW4.pdf
new file mode 100644
index 0000000..2792b80
Binary files /dev/null and b/ME_2046/HW4/S25HW4.pdf differ
diff --git a/ME_2046/HW4/hw4.py b/ME_2046/HW4/hw4.py
new file mode 100644
index 0000000..aeb1b60
--- /dev/null
+++ b/ME_2046/HW4/hw4.py
@@ -0,0 +1,56 @@
+import sympy as sm
+import numpy as np
+import matplotlib.pyplot as plt
+
+sm.init_printing()
+
+print("PROBLEM 1:")
+print("part a:")
+s, z, t = sm.symbols("s z t")
+
+J, B, RHO, RADIUS, L, RESIST, T = sm.symbols(
+    "J, B, rho,  r,  L,  R, T", Real=True, Positive=True
+)
+K_T, K_B = sm.symbols("K_T,  K_b")
+
+# loop gain
+Loop_Gain = K_T * 1 / (J * s + B)
+
+# transfer function from motor current command to linear displacement (ignoring feedback)
+X_over_I = Loop_Gain * RHO / s * RADIUS
+sm.pprint(X_over_I)
+X_over_I = X_over_I.expand().simplify()
+sm.pprint(X_over_I)
+
+print("part b:")
+# recall ZOH_eq
+# G(z) = (1-z**-1) Z{L**-1{G(s)/s}}
+print("Finding inverse laplace of G/s")
+G_s = X_over_I
+sm.pprint(G_s / s)
+g_t = sm.inverse_laplace_transform(G_s / s, s, t)
+sm.pprint(g_t.expand())
+
+# make z substitution subs
+
+G_z = (
+    K_T * T * RADIUS * RHO / B * (z / (z - 1) ** 2)
+    - J * K_T * RADIUS * RHO / B**2
+    + J * K_T * RADIUS * RHO / B**2 * (z / (z - sm.exp(-B / J * T)))
+)
+
+sm.pprint(G_z.simplify())
+
+# part c was on the board
+print("part c")
+F = sm.Matrix([[0, RHO], [0, -B / J]])
+G = sm.Matrix([0, K_T / J])
+
+# part d
+print("part d")
+A = sm.exp(F * T)
+B = sm.integrate(A, (T, 0, T))
+sm.pprint(F)
+sm.pprint(G)
+sm.pprint(A)
+sm.pprint(B)