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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
"\n",
"|string|density (g/m)|tension (kg)|\n",
"|---|---|---|\n",
"|E|0.401|7.28|\n",
"|B|0.708|7.22|\n",
"|G|1.140|7.32|\n",
"|D|2.333|8.41|\n",
"|A|4.466|9.03|\n",
"|E|6.790|7.71|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
"\n",
"a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
"\n",
"b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import Audio\n",
"\n",
"E=10e9\n",
"t=0.04 \n",
"I = (0.04*0.02**3)/12\n",
"L = 0.64\n",
"g = 9.81\n",
"h = 0.004\n",
"\n",
"rho_e = 0.401e-3\n",
"T_e = 7.28*9.81\n",
"rho_b = 0.708e-3\n",
"T_b = 7.22*9.81\n",
"rho_g = 1.140e-3\n",
"T_g = 7.32*9.81\n",
"rho_d = 2.333e-3\n",
"T_d = 8.41*9.81\n",
"rho_a = 4.466e-3\n",
"T_a = 9.03*9.81\n",
"rho_e2 = 6.790e-3\n",
"T_e2 = 7.71*9.81"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"M = (T_e+T_b+T_g+T_d+T_a+T_e2)*h\n",
"x = np.linspace(0,L,100)\n",
"w = (M*L**2/(2*E*I))*(x/L)**2\n",
"\n",
"N = 9\n",
"h1 = L/10\n",
"xnum = np.arange(0,L+h1/2,h1)\n",
"\n",
"A1 = np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A1[0,0]+=1\n",
"A1[-1,-1]+=1\n",
"A1[7]= [0,0,0,0,0,1,-4,5,-2]\n",
"A1[8] = [0,0,0,0,0,0,2,-4,2]\n",
"b1=-np.zeros(N)\n",
"b1[7]=-h1**2*M/(E*I)\n",
"b1[8]=2*h1**2*M/(E*I)\n",
"w1 = np.linalg.solve(A1,b1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"plt.plot(x,w,label='Analytical Sol')\n",
"plt.plot(xnum[:-1],np.block([0,w1]),'ro',label='Numerical Sol')\n",
"plt.ylabel('Delfection [m]')\n",
"plt.xlabel('Length of Beam [m]')\n",
"plt.title('Deflection along Beam')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"h = np.array([L/4,L/8,L/12,L/16,L/24])\n",
"w2 = []\n",
"xnum2 = []\n",
"for i in range(len(h)):\n",
" shape = int(L/h[i])\n",
" A2=np.diag(np.ones(shape)*6)+np.diag(np.ones(shape-1)*-4,-1)\\\n",
" +np.diag(np.ones(shape-1)*-4,1)+np.diag(np.ones(shape-2),-2)+np.diag(np.ones(shape-2),2)\n",
" A2[0,0]+=1\n",
" A2[-1,-1]+=1\n",
" A2[-2]= np.zeros(shape)\n",
" A2[-2,-4:]=[1,-4,5,-2]\n",
" A2[-1] = np.zeros(shape)\n",
" A2[-1,-3:] = [2,-4,2]\n",
" b2=-np.zeros(shape)\n",
" b2[-2]=-h[i]**2*M/(E*I)\n",
" b2[-1]=2*h[i]**2*M/(E*I)\n",
" w2.append(np.linalg.solve(A2,b2))\n",
" xnum2.append(np.arange(0,L+h[i]/2,h[i]))\n",
"plt.figure(figsize=(7,7))\n",
"plt.plot(x,w,label='Analytical Sol')\n",
"plt.plot(xnum2[0],np.block([0,w2[0]]),label='4-Step')\n",
"plt.plot(xnum2[1],np.block([0,w2[1]]),label='8-Step')\n",
"plt.plot(xnum2[2],np.block([0,w2[2]]),label='12-Step')\n",
"plt.plot(xnum2[3],np.block([0,w2[3]]),label='16-Step')\n",
"plt.plot(xnum2[4],np.block([0,w2[4]]),label='24-Step')\n",
"plt.ylabel('Delfection [m]')\n",
"plt.xlabel('Length of Beam [m]')\n",
"plt.title('Convergence of Deflection along Beam')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ana = np.max(w)\n",
"error = []\n",
"for i in range(len(h)):\n",
" num = np.max(w2[i])\n",
" error.append(np.abs(ana-num))\n",
"step = np.array([24,16,12,8,4])\n",
"plt.figure(figsize=(7,7))\n",
"plt.plot(step,error)\n",
"plt.ylabel('Absolute Error from Max Delfection')\n",
"plt.xlabel('Number of Steps of h')\n",
"plt.title('Convergence of Deflection along Beam');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
"\n",
"__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
"\n",
"a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"L = 0.64\n",
"mu = 1.14e-3\n",
"T = 71.81\n",
"\n",
"N6=6 # 6-node guitar string\n",
"dx6=L/(N6+1)\n",
"k6 = T/dx6**2/mu\n",
"A6 = k6*(np.diag(np.ones(N6)*2)\\\n",
" -np.diag(np.ones(N6-1),-1)\\\n",
" -np.diag(np.ones(N6-1),1))\n",
"e6,v6=np.linalg.eig(A6)\n",
"isort = np.argsort(e6.real)\n",
"e6=e6[isort]\n",
"v6=v6[:,isort]\n",
"\n",
"N30=30 # 30-node guitar string\n",
"dx30=L/(N30+1)\n",
"k30 = T/dx30**2/mu\n",
"A30 = k30*(np.diag(np.ones(N30)*2)\\\n",
" -np.diag(np.ones(N30-1),-1)\\\n",
" -np.diag(np.ones(N30-1),1))\n",
"e30,v30=np.linalg.eig(A30)\n",
"isort = np.argsort(e30.real)\n",
"e30=e30[isort]\n",
"v30=v30[:,isort]\n",
"\n",
"N45=45 # 45-node guitar string\n",
"dx45=L/(N45+1)\n",
"k45 = T/dx45**2/mu\n",
"A45 = k45*(np.diag(np.ones(N45)*2)\\\n",
" -np.diag(np.ones(N45-1),-1)\\\n",
" -np.diag(np.ones(N45-1),1))\n",
"e45,v45=np.linalg.eig(A45)\n",
"isort = np.argsort(e45.real)\n",
"e45=e45[isort]\n",
"v45=v45[:,isort]\n",
"\n",
"N60=60 # 60-node guitar string\n",
"dx60=L/(N60+1)\n",
"k60 = T/dx60**2/mu\n",
"A60 = k60*(np.diag(np.ones(N60)*2)\\\n",
" -np.diag(np.ones(N60-1),-1)\\\n",
" -np.diag(np.ones(N60-1),1))\n",
"e60,v60=np.linalg.eig(A60)\n",
"isort = np.argsort(e60.real)\n",
"e60=e60[isort]\n",
"v60=v60[:,isort]\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N6))\n",
"print(e6[:3].real**0.5/2/np.pi)\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N30))\n",
"print(e30[:3].real**0.5/2/np.pi)\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N45))\n",
"print(e45[:3].real**0.5/2/np.pi)\n",
"\n",
"print('Natural frequencies of {}-element string (Hz)'.format(N60))\n",
"print(e60[:3].real**0.5/2/np.pi)\n",
"\n",
"x6 = np.linspace(0,L,N6+2)\n",
"x30 = np.linspace(0,L,N30+2)\n",
"x45 = np.linspace(0,L,N45+2)\n",
"x60 = np.linspace(0,L,N60+2)\n",
"\n",
"plt.figure(figsize=(10,7))\n",
"plt.plot(x6[1:-1],-1*v6[:,0]/np.max(-v6[:,0]),'bo',label='6 node')\n",
"plt.plot(x30[1:-1],-1*v30[:,0]/np.max(-v30[:,0]),'ko',label='30 node')\n",
"plt.plot(x45[1:-1],1*v45[:,0]/np.max(v45[:,0]),'ro',label='45 node')\n",
"plt.plot(x60[1:-1],-1*v60[:,0]/np.max(-v60[:,0]),'go',label='60 node')\n",
"plt.title('First Eigen with Increasing Node Count')\n",
"plt.xlabel('Node Count')\n",
"plt.ylabel('Amplitude')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,7))\n",
"plt.plot(x6[1:-1],1*v6[:,1]/np.max(-v6[:,1]),'bo',label='6 node')\n",
"plt.plot(x30[1:-1],-1*v30[:,1]/np.max(-v30[:,1]),'ko',label='30 node')\n",
"plt.plot(x45[1:-1],1*v45[:,1]/np.max(-v45[:,1]),'ro',label='45 node')\n",
"plt.plot(x60[1:-1],-1*v60[:,1]/np.max(-v60[:,1]),'go',label='60 node')\n",
"plt.title('Second Eigen with Increasing Node Count')\n",
"plt.xlabel('Node Count')\n",
"plt.ylabel('Amplitude')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,7))\n",
"plt.plot(x6[1:-1],-1*v6[:,2]/np.max(-v6[:,2]),'bo',label='6 node')\n",
"plt.plot(x30[1:-1],-1*v30[:,2]/np.max(-v30[:,2]),'ko',label='30 node')\n",
"plt.plot(x45[1:-1],1*v45[:,2]/np.max(-v45[:,2]),'ro',label='45 node')\n",
"plt.plot(x60[1:-1],-1*v60[:,2]/np.max(-v60[:,2]),'go',label='60 node')\n",
"plt.title('Third Eigen with Increasing Node Count')\n",
"plt.xlabel('Node Count')\n",
"plt.ylabel('Amplitude')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Converges at 45 nodes\n"
]
}
],
"source": [
"print('Converges at 45 nodes')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"b. Use the number of nodes necessary for convergence to calculate the first 3 modes of vibration for the other 5 strings on the guitar. Display the first three natural frequencies for all six strings. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"rho_e = 0.401e-3\n",
"T_e = 7.28*9.81\n",
"rho_b = 0.708e-3\n",
"T_b = 7.22*9.81\n",
"rho_g = 1.140e-3\n",
"T_g = 7.32*9.81\n",
"rho_d = 2.333e-3\n",
"T_d = 8.41*9.81\n",
"rho_a = 4.466e-3\n",
"T_a = 9.03*9.81\n",
"rho_e2 = 6.790e-3\n",
"T_e2 = 7.71*9.81"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E-string (Hz)\n",
"[329.63523775 658.88613556 987.36880161]\n"
]
}
],
"source": [
"N_e=45\n",
"dx_e=L/(N_e+1)\n",
"k_e = T_e/dx_e**2/rho_e\n",
"A_e = k_e*(np.diag(np.ones(N_e)*2)\\\n",
" -np.diag(np.ones(N_e-1),-1)\\\n",
" -np.diag(np.ones(N_e-1),1))\n",
"e_e,v_e=np.linalg.eig(A_e)\n",
"isort = np.argsort(e_e.real)\n",
"e_e=e_e[isort]\n",
"v_e=v_e[:,isort]\n",
"\n",
"print('Natural frequencies of E-string (Hz)')\n",
"print(e_e[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of B-string (Hz)\n",
"[247.05411832 493.82018258 740.01047461]\n"
]
}
],
"source": [
"N_b=45\n",
"dx_b=L/(N_b+1)\n",
"k_b = T_b/dx_b**2/rho_b\n",
"A_b = k_b*(np.diag(np.ones(N_b)*2)\\\n",
" -np.diag(np.ones(N_b-1),-1)\\\n",
" -np.diag(np.ones(N_b-1),1))\n",
"e_b,v_b=np.linalg.eig(A_b)\n",
"isort = np.argsort(e_b.real)\n",
"e_b=e_b[isort]\n",
"v_b=v_b[:,isort]\n",
"\n",
"print('Natural frequencies of B-string (Hz)')\n",
"print(e_b[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of G-string (Hz)\n",
"[196.03934499 391.85011687 587.20400904]\n"
]
}
],
"source": [
"N_g=45 # 45-node guitar string\n",
"dx_g=L/(N_g+1)\n",
"k_g = T_g/dx_g**2/rho_g\n",
"A_g = k_g*(np.diag(np.ones(N_g)*2)\\\n",
" -np.diag(np.ones(N_g-1),-1)\\\n",
" -np.diag(np.ones(N_g-1),1))\n",
"e_g,v_g=np.linalg.eig(A_g)\n",
"isort = np.argsort(e_g.real)\n",
"e_g=e_g[isort]\n",
"v_g=v_g[:,isort]\n",
"\n",
"print('Natural frequencies of G-string (Hz)')\n",
"print(e_g[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E-string (Hz)\n",
"[146.88611909 293.60097554 439.97350639]\n"
]
}
],
"source": [
"N_d=45\n",
"dx_d=L/(N_d+1)\n",
"k_d = T_d/dx_d**2/rho_d\n",
"A_d = k_d*(np.diag(np.ones(N_d)*2)\\\n",
" -np.diag(np.ones(N_d-1),-1)\\\n",
" -np.diag(np.ones(N_d-1),1))\n",
"e_d,v_d=np.linalg.eig(A_d)\n",
"isort = np.argsort(e_d.real)\n",
"e_d=e_d[isort]\n",
"v_d=v_d[:,isort]\n",
"\n",
"print('Natural frequencies of E-string (Hz)')\n",
"print(e_d[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E-string (Hz)\n",
"[110.00809489 219.88792527 329.51137616]\n"
]
}
],
"source": [
"N_a=45\n",
"dx_a=L/(N_a+1)\n",
"k_a = T_a/dx_a**2/rho_a\n",
"A_a = k_a*(np.diag(np.ones(N_a)*2)\\\n",
" -np.diag(np.ones(N_a-1),-1)\\\n",
" -np.diag(np.ones(N_a-1),1))\n",
"e_a,v_a=np.linalg.eig(A_a)\n",
"isort = np.argsort(e_a.real)\n",
"e_a=e_a[isort]\n",
"v_a=v_a[:,isort]\n",
"\n",
"print('Natural frequencies of E-string (Hz)')\n",
"print(e_a[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of E-string (Hz)\n",
"[ 82.43894585 164.78177157 246.93246912]\n"
]
}
],
"source": [
"N_e2=45\n",
"dx_e2=L/(N_e2+1)\n",
"k_e2 = T_e2/dx_e2**2/rho_e2\n",
"A_e2 = k_e2*(np.diag(np.ones(N_e2)*2)\\\n",
" -np.diag(np.ones(N_e2-1),-1)\\\n",
" -np.diag(np.ones(N_e2-1),1))\n",
"e_e2,v_e2=np.linalg.eig(A_e2)\n",
"isort = np.argsort(e_e2.real)\n",
"e_e2=e_e2[isort]\n",
"v_e2=v_e2[:,isort]\n",
"\n",
"print('Natural frequencies of E-string (Hz)')\n",
"print(e_e2[:3].real**0.5/2/np.pi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
"\n",
"_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samplerate = 20000\n",
"t = np.arange(0,3,1/samplerate)\n",
"data = 100*(np.sin(t*e_e[0].real**0.5)+np.sin(t*e_b[0].real**0.5)+np.sin(t*e_g[0].real**0.5)+\n",
" np.sin(t*e_d[0].real**0.5)+np.sin(t*e_a[0].real**0.5)+np.sin(t*e_e2[0].real**0.5)+\n",
" np.sin(t*e_e[1].real**0.5)+np.sin(t*e_b[1].real**0.5)+np.sin(t*e_g[1].real**0.5)+\n",
" np.sin(t*e_d[1].real**0.5)+np.sin(t*e_a[1].real**0.5)+np.sin(t*e_e2[1].real**0.5)+\n",
" np.sin(t*e_e[2].real**0.5)+np.sin(t*e_b[2].real**0.5)+np.sin(t*e_g[2].real**0.5)+\n",
" np.sin(t*e_d[2].real**0.5)+np.sin(t*e_a[2].real**0.5)+np.sin(t*e_e2[2].real**0.5))\n",
"Audio(data=data,rate=samplerate)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
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