Determine if the following functions satisfy the Dirichlet conditions and have CTFS representation
![(a)-(t)-, t = (0, 2] and x(t) = z(t + 2); b) (t)cos(/2t), t -(,1 and«(t) - and (t)-x(t (e) (t) -in(ln(t),t (0,1] and z(t) - 0](http://img.homeworklib.com/images/9f5a8518-e7ab-4702-a90e-c564b0cd4659.png?x-oss-process=image/resize,w_560)
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Determine if the following functions satisfy the Dirichlet conditions and have CTFS representation
1. For the three following signal sets . Find the basis functions using Gram-Schmidt method. ....
1. For the three following signal sets . Find the basis functions using Gram-Schmidt method. . Plot the corresponding signal space representation. . Find the distance between the two signals. (a) x(t) = Acos(2tht), y(t) = Asin(2T,fet), t E [0, e). [30 points] (b) (t) A cos(2m fct), y(t) A cos(2m fct+0), t E [0, Tb]. [30 points] (c) The signal set shown in Figure 1 [40 points xp V3A T/2 T To
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....
solve for a and b 1. Plot each of the following functions and find its Fourier series representation, also determine...
solve for a and b
1. Plot each of the following functions and find its Fourier series representation, also determine the first three One zero harmonics (a) f(t) -1<t< T= 2 where T is the period. 0t<1 J (b) f(t) -t-1<t<0 T 4 where T is the poriod = 0t1 0-2<t<-1 T = 4 where T is the period (e) g(t) 1 -1<t<1 0 1<t<2 (d) g(t) = 1- t -1<t<1;T = 4 where T is the period
1. Plot...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1,...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1, 2): (8 points) tut(t, z) - trọt, c) = c+t, (t, x) R x [0, +x), u(0, 2) = cos(V), 4(0,2)=e", u(t,0) = 1+ t.
8. Let f and g be scalar functions with continuous partial derivatives, and let C and S satisfy the conditions of St...
8. Let f and g be scalar functions with continuous partial derivatives, and let C and S satisfy the conditions of Stokes's Theorem. Verify each identity. (a) dr = Vg) N ds X (b) dr 0 (e)
8. Let f and g be scalar functions with continuous partial derivatives, and let C and S satisfy the conditions of Stokes's Theorem. Verify each identity. (a) dr = Vg) N ds X (b) dr 0 (e)
(3) Determine by substitution which of the functions ya(t) = A e(-2+6j)t, yo(t) = B e(2+63)t,...
(3) Determine by substitution which of the functions ya(t) = A e(-2+6j)t, yo(t) = B e(2+63)t, yo(t) =C e(-2-63)t satisfy the DE y" +4y'+40 y = 0, where A, B, C are nonzero constants. (4) Let y(t) = 0 + A e(-2-63)t + Be(-2+63)t, and use Euler's identity to show that y(t) = 0) + C e 2t sin (6t) + De-2t cos (6 t), where C =j(B-A) and D equals something similar. Then find constants C, D such that...
ONLY NUMBER 2 1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise...
ONLY NUMBER 2
1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise from the CTFS coefficients of a(t) from the previous problem. (a) What is the periodic convolution of r(t) with itself? (b) How is the periodic convolution of r(t) with itself related to y(t) (c) Find the coefficients of y(t) by applying CTFS properties, selected...
Consider a potential problem in the half-space defined by 2 20, with Dirichlet boundary conditions on...
Consider a potential problem in the half-space defined by 2 20, with Dirichlet boundary conditions on the plane z = 0 and at infinity). (a) Write down the appropriate Green function G(x, x'). (b) If the potential on the plane z = 0 is specified to be 0 Vinside a circle of radius a centered at the origin, and Ø = 0 outside that circle, find an integral expression for the potential at the point P specified in terms of...
need help all those questions. 10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b...
need help all those questions.
10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, ...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
1. For the three following signal sets . Find the basis functions using Gram-Schmidt method. . Plot the corresponding signal space representation. . Find the distance between the two signals. (a) x(t) = Acos(2tht), y(t) = Asin(2T,fet), t E [0, e). [30 points] (b) (t) A cos(2m fct), y(t) A cos(2m fct+0), t E [0, Tb]. [30 points] (c) The signal set shown in Figure 1 [40 points xp V3A T/2 T To
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....
solve for a and b
1. Plot each of the following functions and find its Fourier series representation, also determine the first three One zero harmonics (a) f(t) -1<t< T= 2 where T is the period. 0t<1 J (b) f(t) -t-1<t<0 T 4 where T is the poriod = 0t1 0-2<t<-1 T = 4 where T is the period (e) g(t) 1 -1<t<1 0 1<t<2 (d) g(t) = 1- t -1<t<1;T = 4 where T is the period
1. Plot...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1, 2): (8 points) tut(t, z) - trọt, c) = c+t, (t, x) R x [0, +x), u(0, 2) = cos(V), 4(0,2)=e", u(t,0) = 1+ t.
8. Let f and g be scalar functions with continuous partial derivatives, and let C and S satisfy the conditions of Stokes's Theorem. Verify each identity. (a) dr = Vg) N ds X (b) dr 0 (e)
8. Let f and g be scalar functions with continuous partial derivatives, and let C and S satisfy the conditions of Stokes's Theorem. Verify each identity. (a) dr = Vg) N ds X (b) dr 0 (e)
(3) Determine by substitution which of the functions ya(t) = A e(-2+6j)t, yo(t) = B e(2+63)t, yo(t) =C e(-2-63)t satisfy the DE y" +4y'+40 y = 0, where A, B, C are nonzero constants. (4) Let y(t) = 0 + A e(-2-63)t + Be(-2+63)t, and use Euler's identity to show that y(t) = 0) + C e 2t sin (6t) + De-2t cos (6 t), where C =j(B-A) and D equals something similar. Then find constants C, D such that...
ONLY NUMBER 2
1. Find the CTFS coefficients of the periodic signal 1 1-4 」E [0, 1] 0 otherwise 2. In this problem you will practice using properties to derive the CTFS coefficients of 0 otherwise from the CTFS coefficients of a(t) from the previous problem. (a) What is the periodic convolution of r(t) with itself? (b) How is the periodic convolution of r(t) with itself related to y(t) (c) Find the coefficients of y(t) by applying CTFS properties, selected...
Consider a potential problem in the half-space defined by 2 20, with Dirichlet boundary conditions on the plane z = 0 and at infinity). (a) Write down the appropriate Green function G(x, x'). (b) If the potential on the plane z = 0 is specified to be 0 Vinside a circle of radius a centered at the origin, and Ø = 0 outside that circle, find an integral expression for the potential at the point P specified in terms of...
need help all those questions.
10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
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