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index 0000000..ae499a2 --- /dev/null +++ b/NUCE_2113/lab6/quick_maths.py @@ -0,0 +1,61 @@ +print("Experiment 6.1\n") +measured_activity = 5.2e-6 # curies +elapsed_time = 193.92 # s +sigma_u1 = 35331 # counts +background_time = 193.94 # s +sigma_b = 558 # counts + +R = sigma_u1 / elapsed_time - sigma_b / background_time +print(f"R: {R:.3e} counts / s") +print(f"R: {R/3.7e10*1e6:.3e} microcurie") +eps_ip = 0.101 # from figure 6.2 +f = 0.6617 + +d = 100 # mm +r = 38 / 2 # mm + +G = r**2 / 4 / d**2 + +A = R / eps_ip / G / f + +print(f"G: {G:.3e}") +print(f"A: {A:.3e} decays / s") +print(f"A: {A/3.7e10*1e6:.3e} microcurie") + +A = 4.5 * 3.7e10 / 1e6 +eps_ip_est = R / A / G / f +print(f"eps_ips: {eps_ip_est:.3e}") + +sigma_u1 = [10122, 11763, 14464, 17476, 22073, 28268, 38084] +sigma_b = 130 +d = [100, 90, 80, 70, 60, 50, 40] +t = 60 # s + +import numpy as np + +n = len(sigma_u1) +R = np.empty(n) +G = np.empty(n) +eps_ip = np.empty(n) + +for i, value in enumerate(sigma_u1): + print(i, value) + R[i] = (value - sigma_b) / t + G[i] = r**2 / 4 / d[i] ** 2 + eps_ip[i] = R[i] / A / G[i] / f + +print("R") +print(R.transpose()) +print("G") +print(G.transpose()) +print("eps_ip") +print(eps_ip.transpose()) + +import matplotlib.pyplot as plt + +plt.plot(d, eps_ip, ".b") +plt.xlabel("Distance [mm]") +plt.ylabel("$\epsilon_{ip}$") +plt.grid("both") +plt.savefig("exercise6_4.png") +plt.show() From 802118c5677adb69fc161fe085efbb5dd56f19d4 Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Wed, 12 Mar 2025 15:35:14 -0400 Subject: [PATCH 2/5] me2046 hw4 --- ME_2046/HW4/S25HW4.pdf | Bin 0 -> 229582 bytes ME_2046/HW4/hw4.py | 56 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 56 insertions(+) create mode 100644 ME_2046/HW4/S25HW4.pdf create mode 100644 ME_2046/HW4/hw4.py diff --git a/ME_2046/HW4/S25HW4.pdf b/ME_2046/HW4/S25HW4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2792b803c747fc339d70af4ed5afdadade7e7610 GIT binary patch literal 229582 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z%MFFx94i2O3RsgH`2iyZ5a#XYvhaYwH}65f(7`}A>&pYQ)vq!j!yEYl-FtJ+00zP! z^4=^96fg)kuQe#|FZKX15x?9sfX#;e(xxyjZouXFxo$9E!|cuS!JyEa_8ts_0+qX& z7AVZkcIM@V^4{z>z(V}e=e*qT>&K0QXJ12FQTFpU(@(ez`A!F@*<+QTbE(02%L1 zyUWD|+zmI{0FZ&eH?Au{#sj@^odP!z*Uk9`Fdo5w9m{~(?=Sg5uf6d9mJe9E0iJ2Q zV({|=p1F;$#q|W5np4%u$({OoxTIF4=9F=?bOOXcqyP3z9M~YiZ)pZhjd*}@!qmhP y#A^opLo8vYARZV9W@ZM3fCVxBS>^ZT9XEHtKlp9(&cy}H*5MfR^b$&v82=9k(k Date: Thu, 13 Mar 2025 16:05:45 -0400 Subject: [PATCH 3/5] me 2046 hw4 complete! --- ME_2046/HW4/hw4.py | 76 +++++++++++++++++- .../Project/ME2046 - Project Description.pdf | Bin 0 -> 74913 bytes 2 files changed, 74 insertions(+), 2 deletions(-) create mode 100644 ME_2046/Project/ME2046 - Project Description.pdf diff --git a/ME_2046/HW4/hw4.py b/ME_2046/HW4/hw4.py index aeb1b60..f516618 100644 --- a/ME_2046/HW4/hw4.py +++ b/ME_2046/HW4/hw4.py @@ -33,13 +33,13 @@ sm.pprint(g_t.expand()) # make z substitution subs -G_z = ( +G_z = (1 - z**-1) * ( 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()) +sm.pprint(G_z) # part c was on the board print("part c") @@ -54,3 +54,75 @@ sm.pprint(F) sm.pprint(G) sm.pprint(A) sm.pprint(B) + +########################################################a +print("PROBLEM 4:") +print("bilinear transform") +T = 0.2 # s + +G_s = 10 / (s + 10) +G_z = G_s.subs(s, 2 * (z - 1) / T * (z + 1)) +sm.pprint(G_z) +sm.pprint(G_z.simplify()) + +print("bilinear with warping") +omega_star = 10 # rad/s +G_z_warped = G_s.subs(s, (omega_star / np.tan(omega_star * T / 2)) * (z - 1) / (z + 1)) +sm.pprint(G_z_warped) +sm.pprint(G_z_warped.simplify()) + +# Create a frequency vector from 0 to 10 rad/s (avoid exactly 0 to prevent log(0) issues) +omega = np.linspace(5, 15, 500) + +# Continuous-time frequency response (evaluate at s = j*omega) +G_s_response = 10 / (10 + 1j * omega) + +# For the discrete transfer functions, substitute z = exp(j*omega*T) +z_vals = np.exp(1j * omega * T) + +# Convert symbolic expressions into functions that accept numpy arrays +G_z_func = sm.lambdify(z, G_z, "numpy") +G_z_warped_func = sm.lambdify(z, G_z_warped, "numpy") + +G_z_response = G_z_func(z_vals) +G_z_warped_response = G_z_warped_func(z_vals) + + +# Helper function to compute magnitude (in dB) and phase (in degrees) +def compute_mag_phase(response): + mag = 20 * np.log10(np.abs(response)) + phase = np.angle(response, deg=True) + return mag, phase + + +# Compute responses +mag_s, phase_s = compute_mag_phase(G_s_response) +mag_z, phase_z = compute_mag_phase(G_z_response) +mag_z_warped, phase_z_warped = compute_mag_phase(G_z_warped_response) + +# Plot the Bode plots +plt.figure(figsize=(10, 8)) + +# Magnitude plot +plt.subplot(2, 1, 1) +plt.semilogx(omega, mag_s, label="Continuous: G(s)") +plt.semilogx(omega, mag_z, label="Bilinear: G(z)") +plt.semilogx(omega, mag_z_warped, label="Warped: G(z)_warped") +plt.title("Bode Magnitude Plot") 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zAcUjh?=mUyKV)DKk`P#bwEM30y9^A4f&XO;f)&5FgF>OOKkb7fC8Y=%tna=4W%G~H z?=l1g3H`G_kQ4;=r!E)@h7nftxBkF{bQ1JW859C198P|32bClo5dM%!LScW73x-NT z|Dj9Bo`L_+g-S|F{^>7aIS_x^M;I3Qryp=6oRE(D-4-}f3i;=_2q;wQ&;AgEQ2Wzg z1QZVab1e~2B=VOrJaK43at!x9J*n^LhatooP(lxjC8Xnip4>Ft?68DH*!RPegoX<6 zGEfF>i-aNUq>vb>Bw7+~jl{qa1gAkrFxm!VgNDH50RO$okCP$Zlki6R9_0v0Fia94 KAfT$N2KXOdlnloJ literal 0 HcmV?d00001 From 7f74985468b6a7f78bee0e54d658a1d6e7dde37f Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 17 Mar 2025 10:51:57 -0400 Subject: [PATCH 4/5] idk --- ME_2046/HW4/hw4.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/ME_2046/HW4/hw4.py b/ME_2046/HW4/hw4.py index f516618..ff97b00 100644 --- a/ME_2046/HW4/hw4.py +++ b/ME_2046/HW4/hw4.py @@ -72,7 +72,7 @@ sm.pprint(G_z_warped) sm.pprint(G_z_warped.simplify()) # Create a frequency vector from 0 to 10 rad/s (avoid exactly 0 to prevent log(0) issues) -omega = np.linspace(5, 15, 500) +omega = np.linspace(0, 10, 500) # Continuous-time frequency response 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