can please explain why F(sigma)= u?
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can please explain why F(sigma)= u?
We consider the PDE: for given o(t) € H|(12) find...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) =...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Can anyone help with this question please? Given a domain Ω c R2 and a smooth function f,uo : Ω-+ R consider the proble...
Can anyone help with this question please?
Given a domain Ω c R2 and a smooth function f,uo : Ω-+ R consider the problem Uz (x, t)-Au (x, t) + u(x, t) u(x, t = f(x) Y(x, t) E Ω × (0, oo), V(x, t) E 2 x (0, 00), Assume that u(z, t) is a smooth solution and that v(x) is a smooth stationary (i.e., time-independent) solution. Derive a PDE problem for the difference w(x, t)u(x, t)(x) By multiplying...
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The sol...
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The solution w(r, t) to the homogenized PDE wt-Wra, with w(0,t,t)0 1S -1 Verify that ugen(x, t)Ue(x) +w(x, t) solves the full PDE and BCs (c) Let u(x,0)- f(x) - 2 - ^2 be the initial condition. Find the particular solution by specifying all Fourier coefficients
3. Consider the...
solution help, tq. What is the Inverse Fourier transform of Your answer should be expressed as a function of t using the correct syntax. Inverse FT. is f(t) = Skipped F(u)-(15ru2 +4ιτω4)sgn(a)? Find...
solution help, tq.
What is the Inverse Fourier transform of Your answer should be expressed as a function of t using the correct syntax. Inverse FT. is f(t) = Skipped F(u)-(15ru2 +4ιτω4)sgn(a)? Find the Inverse Fourier transform of: F(u)--8πΗ(w+5)-H(w-5) e- Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is ft)Skipped 8iu Find the Inverse Fourier transform of: F(w) 16 πυ) sgn(w)e-20 Your answer should be expressed as a function of t using...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and i...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and initial conditions (b) Using separation of variables find the displacement u(z,t) for any 0 < z < L, and t > 0. (c) Using values of L = 65 cm, a 15 cm and c-10 cm/sec, produce a surface plot of your solution over the length of the string and the time interval 0<t<10. Include the first 20 terms of your series...
thank you for the help :) Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using...
thank you for the help :)
Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax f() Skipped
Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms....
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skippe...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
please solve, previous ones all wrong! Question 11 1 mark) Attempt 2 What is the Inverse Fourier transform of F(u)- 10-5? Reflection: F-1[F(-u)]=f(-t) Your answer should be expressed as a function of...
please solve, previous ones all wrong!
Question 11 1 mark) Attempt 2 What is the Inverse Fourier transform of F(u)- 10-5? Reflection: F-1[F(-u)]=f(-t) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 12 (T mark) Attempt 2 What is the Inverse Fourier transform of: 7 16+iw-4)2 Reflection: F--) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 13 (2 marks)...
Mark which statements below are true, using the following Consider the diffusion problem u(0,t)=0...
Mark which statements below are true, using the following Consider the diffusion problem u(0,t)=0, u(L,t)=50 where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two u(z,t) = X(z)T(t) + us(z), where the subscript designates the function as the steady limit and does not represent a derlvative. BEWARE: MARKING A STATEMENT TRUE...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Can anyone help with this question please?
Given a domain Ω c R2 and a smooth function f,uo : Ω-+ R consider the problem Uz (x, t)-Au (x, t) + u(x, t) u(x, t = f(x) Y(x, t) E Ω × (0, oo), V(x, t) E 2 x (0, 00), Assume that u(z, t) is a smooth solution and that v(x) is a smooth stationary (i.e., time-independent) solution. Derive a PDE problem for the difference w(x, t)u(x, t)(x) By multiplying...
3. Consider the non homogeneous heat equation ut- urr+ 1 with non homogeneous boundary conditions u(0. t) 1, u(1t) (a) Find the equilibrium solution ueqx) to the non homogeneous equation. (b) The solution w(r, t) to the homogenized PDE wt-Wra, with w(0,t,t)0 1S -1 Verify that ugen(x, t)Ue(x) +w(x, t) solves the full PDE and BCs (c) Let u(x,0)- f(x) - 2 - ^2 be the initial condition. Find the particular solution by specifying all Fourier coefficients
3. Consider the...
solution help, tq.
What is the Inverse Fourier transform of Your answer should be expressed as a function of t using the correct syntax. Inverse FT. is f(t) = Skipped F(u)-(15ru2 +4ιτω4)sgn(a)? Find the Inverse Fourier transform of: F(u)--8πΗ(w+5)-H(w-5) e- Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is ft)Skipped 8iu Find the Inverse Fourier transform of: F(w) 16 πυ) sgn(w)e-20 Your answer should be expressed as a function of t using...
That is u(x,0)-f(x) where f(x) (L-x)/(L-a), a<x<L. (a) State the problem including the PDE and all boundary and initial conditions (b) Using separation of variables find the displacement u(z,t) for any 0 < z < L, and t > 0. (c) Using values of L = 65 cm, a 15 cm and c-10 cm/sec, produce a surface plot of your solution over the length of the string and the time interval 0<t<10. Include the first 20 terms of your series...
thank you for the help :)
Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax f() Skipped
Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms....
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
please solve, previous ones all wrong!
Question 11 1 mark) Attempt 2 What is the Inverse Fourier transform of F(u)- 10-5? Reflection: F-1[F(-u)]=f(-t) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 12 (T mark) Attempt 2 What is the Inverse Fourier transform of: 7 16+iw-4)2 Reflection: F--) Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) Question 13 (2 marks)...
Mark which statements below are true, using the following Consider the diffusion problem u(0,t)=0, u(L,t)=50 where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two u(z,t) = X(z)T(t) + us(z), where the subscript designates the function as the steady limit and does not represent a derlvative. BEWARE: MARKING A STATEMENT TRUE...
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