1.[10pt] Compute the convolution X(t)* v(t). x(t) = 2u(t) – 2u(t – 2), s 2-t, 0<t<2...
Compute the convolution using the CONVOLUTIONAL SUM method Problem 2.19. Compute the convolution y(n) of the signals -3< < 1 (n) = Ja". 0 . Otherwise hin) = w Si, 0<n<4 0 otherwise where a is a given parameter.
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
u =<4, -5 > v=<3, 2 > | 2u – vl = ? Whole number. <7, -1, 5 >.< 2, 3, 1>=? whole number
Find the solution to the heat equation on the infinite domain ∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,0,|x|<1|x|>1.∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,|x|<10,|x|>1. in terms of the error function. Q1 (10 points) Find the solution to the heat equation on the infinite domain azu ди at k -00<x<0, t>0, ar2 u(x,0) (X, 1x < 1 10, [] > 1. in terms of the error function. + Drag and drop your files or click to browse...
QUESTION 14 If (S-1) <0, and (T - G) <0, then (M - X)>0 True False
solve with steps and please write as clear as possible. Determine, analytically, the convolution y(t)-r(t) * h(t), where a(t)0, otherwise, and h(t) 1, 1<t < 3 o, otherwise.
(2) The circuit is at steady state for t<0. Find v(t) for t>0. Answer t=0 ZF Navt)14 T
1. problem 2. and 3. as follows Find the inverse Laplace transforms of the following function: 2w7 F(s) = s($2 + 2Cwns + wa) "US 25 (0<5<1) Solve the following differential equation: * + 2wni+wn?x=0, (0) = a, (0) = b where a and b are constants, and 0 << < 1. Solve the following differential equation: ö + 3 + 40 = 2 sint, x(0) = 0, 0) = 0
2. Consider an electron in a 1D potential box (V(x) = 0 for 0<x<L, V(x) = co otherwise) of length L = 1 nm. The electron is described by the wave function, c) = Jasin ( (a) Using the appropriate Hamiltonian derive an expression for the kinetic energy of the electron (5 marks) (b) Calculate the energy (in Joules) of the transition between the ground state and the 1 excited state. [3 marks]
x(0)=1, x'O)= 0, where f(t) = 1 if t< 2; and f(t) = 0 if Find the solution of X"' + 2x' + x=f(t), t> 2.