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(a) For the functions in Figure 1, choose correct values of the constants A. t, and...
For each pair of functions in Figure E.8 D provide the values of the constants A,...
For each pair of functions in Figure E.8 D provide the values of the constants A, to and w in the functional transformation g2(t) = Ag ((t - to)/w). (b) (b) (3) 820) 0-6797 -2 0 2 4 -2 0 2 4 08 821) 0-6797 -2 0 2 4 4 -2 0 2 4 Figure E.8
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If...
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- o+ 0 2 6 8 10 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = u(t - 4) + (31 - 12)114,5(t)}-( - 36 + 18)|15,6 (t) + u(t-6) O B. g(t) = (3-12)114,5(t)+(-3t+18)15,6(t) O c. g(t)...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-1...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-1 0- 0 2 8 10 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = u(t - 4) + (31 - 12)114,6(t)+(-3t+24)116,8(t) + u(t - 8) OB. g(t) = (3-4)u(t - 4)+(-3t+8)u(t-8) O c. g(t) = (3t-12)114,8(t)+(-3t+24)u(t-6) O...
Choose the correct snapshot graph of the string at time t = 1.25 s. Review Constants...
Choose the correct snapshot graph of the string at time t = 1.25 s. Review Constants Periodic Table (Figure 1) is a snapshot graph at t 0 s of a pulse on a string moving to the right at 1 m/s. The string is fixed at -3 m (cm) 2A Figure 〈 1 of 1 〉 2 2A y (cm) at t0 1 m/s Fixed end 0 x (m) y (cm) -A 0 x (m) 2 y (cm) 0 -x...
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions...
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) - f(kx -wt) where k and w are positive constants....
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10 t - CC Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = (3-2)u(t-2)+(-3t+4)u(t-4) OB. g(t) = (3-6)112,3(t)+(-3t+12)813,4(t) OC. g(t) = (3-6)112,4(t)+(-3t+12)u(t - 3) D. g(t) = u(t-2)+(3-6)/12,3(t)+(-3t+ 12)813,4(t) + ut - 4) Compute the Laplace transform of g(t). ${g}= (Type an expression using s as the variable.)
Choose a correct snapshot graph showing the string at t 3 s ReviewI Constants Periodic Table...
Choose a correct snapshot graph showing the string at t 3 s ReviewI Constants Periodic Table (Figure 1) shows a snapshot graph at t = 0 s of two waves approaching each other at 1 m/s v (cm) 1 m/s Figure 1 of 1 x (m) 2 4/6810 1 m/s y (cm) at 0 l m/s y (cm) 1 m/s 0 r (m 2 46810 1 m/s r (m) 2 46810 1 m/s y (cm) 1- 1 m/s 0 4x...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t, ) te (0, o0) (0,3); дли(t, 2) хе _ with boundary conditions ut, 0) 0 u(t, 3) 0 and with initial condition 3 9 u(0, ar) f(x){ 5, | 4' 4 0, Те The solution u of the problem above, with the conventions given in class, has the form ()n "(2)"п (г)"а "," n-1 with the normalization conditions 3 Wn 2n vn (0) 1,...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- O A. g(t) = u(t-1)+(77-7)111,2(t) +(-7t+21)112,3(t) + u(t - 3) B. g(t) = (7t - 7)111,2(t) +(-7t+21)112,3(t) C. g(t) = (77–7)114,3(t) +(-7t+21)u(t-2) Click to select your answer(s). x Ag(t) 1044 0+ 0 2 4 6 00- 10 OK Compute the Laplace transform of g(t). L{g} = (Type an expression using s as the variable.) Click to select your answer(s).
For each pair of functions in Figure E.8 D provide the values of the constants A, to and w in the functional transformation g2(t) = Ag ((t - to)/w). (b) (b) (3) 820) 0-6797 -2 0 2 4 -2 0 2 4 08 821) 0-6797 -2 0 2 4 4 -2 0 2 4 Figure E.8
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- o+ 0 2 6 8 10 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = u(t - 4) + (31 - 12)114,5(t)}-( - 36 + 18)|15,6 (t) + u(t-6) O B. g(t) = (3-12)114,5(t)+(-3t+18)15,6(t) O c. g(t)...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-1 0- 0 2 8 10 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = u(t - 4) + (31 - 12)114,6(t)+(-3t+24)116,8(t) + u(t - 8) OB. g(t) = (3-4)u(t - 4)+(-3t+8)u(t-8) O c. g(t) = (3t-12)114,8(t)+(-3t+24)u(t-6) O...
Choose the correct snapshot graph of the string at time t = 1.25 s. Review Constants Periodic Table (Figure 1) is a snapshot graph at t 0 s of a pulse on a string moving to the right at 1 m/s. The string is fixed at -3 m (cm) 2A Figure 〈 1 of 1 〉 2 2A y (cm) at t0 1 m/s Fixed end 0 x (m) y (cm) -A 0 x (m) 2 y (cm) 0 -x...
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) - f(kx -wt) where k and w are positive constants....
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10 t - CC Express g(t) using window and step functions. Choose the correct answer below. O A. g(t) = (3-2)u(t-2)+(-3t+4)u(t-4) OB. g(t) = (3-6)112,3(t)+(-3t+12)813,4(t) OC. g(t) = (3-6)112,4(t)+(-3t+12)u(t - 3) D. g(t) = u(t-2)+(3-6)/12,3(t)+(-3t+ 12)813,4(t) + ut - 4) Compute the Laplace transform of g(t). ${g}= (Type an expression using s as the variable.)
Choose a correct snapshot graph showing the string at t 3 s ReviewI Constants Periodic Table (Figure 1) shows a snapshot graph at t = 0 s of two waves approaching each other at 1 m/s v (cm) 1 m/s Figure 1 of 1 x (m) 2 4/6810 1 m/s y (cm) at 0 l m/s y (cm) 1 m/s 0 r (m 2 46810 1 m/s r (m) 2 46810 1 m/s y (cm) 1- 1 m/s 0 4x...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t, ) te (0, o0) (0,3); дли(t, 2) хе _ with boundary conditions ut, 0) 0 u(t, 3) 0 and with initial condition 3 9 u(0, ar) f(x){ 5, | 4' 4 0, Те The solution u of the problem above, with the conventions given in class, has the form ()n "(2)"п (г)"а "," n-1 with the normalization conditions 3 Wn 2n vn (0) 1,...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- O A. g(t) = u(t-1)+(77-7)111,2(t) +(-7t+21)112,3(t) + u(t - 3) B. g(t) = (7t - 7)111,2(t) +(-7t+21)112,3(t) C. g(t) = (77–7)114,3(t) +(-7t+21)u(t-2) Click to select your answer(s). x Ag(t) 1044 0+ 0 2 4 6 00- 10 OK Compute the Laplace transform of g(t). L{g} = (Type an expression using s as the variable.) Click to select your answer(s).
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