H.W: (I) - Find the inverse Laplace transform of: s+5 s²+2s +5 1. F(s) 4. F(s) 1 s² + 4s 2s² + 3s +2 (s + 1)³ 2. F(s) 5. F(s) - 6 s2-8s+25 3. F(s) 6. F(s): s+1 s²2s-15 H s²-3s +7 S4 + 5s² +4

Q: B/Express f(x) = cos wx, -1 < x < π, as a Fourier series. Hence prove that 2w π(W² - 1²) cot wπ = +…

A: Given, Function of x is f(x) =cosωx

Q: Find the coefficient of Fourier series of the following voltage waveform. Dr. 28 -3T/2 -T -T/2 T/2…

A:

Q: find the fourier transform. x (t)=√(t) x(t) 62(t) x(t) = 6(t-3) x(t) = 5(2 t)

A:

Q: A Lambertian source of radiance 10 W /m² sr is made in the shape of a ring. What is the irradiance…

A: Given, Lambertian source of radiance= 10 W/m2 srθin= arc sin 0.25θout= arc sin0.5

Q: 9. Show the Complex Fourier Integral Transform (Fourier transform) of the function defined below…

A: We know that the exponential formula of trigonometry of sinA  sinA=[e(iA)-e(-iA)]÷(2i) By using this…

Q: -iwit, The wave function is given by (x, t) = c[3e-i@it&1(x) + 4e-iw2t¢2(x)] where 1(x) and 2(x) are…

A: So we will basically calculate the average of energy by doing normalization. Then the square of the…

Q: Find the Fourier transform of e=jt

A: Given that:f(t)=e-jtTo determine the Fourier transformation of f(t)

Q: Calculate resonance frequency and it's energy a C mg Calculate resonance frequency.

A:

Q: 3. Given the initial wavefunction ¥ (x, 0) = A x exp (- k x ) with x > 0 and k > 0, and ¥ (x, 0) = 0…

A:

Q: Q: Expand g(t) using the sine-cosine Fourier series on the interval -1 <t<1. g(t): V3 %3D

A:

Q: Question 1. The function f(t) is defined as follows f(e) - -1+ 4t +t,0 <ts 8. Let f(t) be the odd…

A: Given the function ft=-1+4t+t2,  0&lt;t≤8 Now, we shall define f^t which is an even periodic…

Q: Find the fourier transform of f(x) defined by f(x) = { = ( and hence evaluate +∞ sin pacos pl du |x|

A:

Q: as where Show that the solution of the Maxwell equation can be obtained 1 V(r.t) = f(r.fr) dr',…

A:

Q: 32. Check the normalization of ψ0 and ψ1 for the harmonic oscillator and prove they are orthogonal.…

A: To find the normalization constant C0 and C1 and check the orthogonality of the two wavefuction

Q: H.W: Calculate the ratio of energy of the frequency range (10→20) Hz up to total enelgy dn2 For the…

A: Given data- f(t)=-t     -0.5&lt;t&lt;0t        0&lt;t&lt;0.50       elsewhereThe graph for the…

Q: I E V(x) Vo X=0 II Q/Solve the Schrödinger equation for regions x0 to calculate the reflection…

A:

Q: (b) A periodic square wave (for example, a diffraction grating, electron density in a 1D crystal)…

A: Given A periodic square wave  can be represented as a convolution between a square pulse and an…

Q: Find the Fourier transform of e-a²t² Hint: Use the integral formula Sе-¹² du = √

A:

Q: Consider a wavefunction defined by: xL The product of the normalisation constant A and , 52 is equal…

A: In this problem, we will use the normalisation condition to calculate the value of A

Q: Find the Fourier Transform for each of the following 2-D continuous functions. a) 1+ 8(x,y) b)…

A:

Q: Solve F[Re[g(t)]] using the Fourier Transform Properties

A:

Q: Question # 01: Given a potential of the form: 0, * a/2. Derive the conditions for maximum…

A:

Q: Find the Fourier transform of rect(t/4). (a) sinc(w) (b) sinc(w) (c) sinc(2w) (d) 2 sinc(2w)

A:

Q: For the amplitude and phase spectrum shown in figure below, The Compact Fourier series is: 3 456 7 8…

A:

Q: VatuablelEL J choose the answet 31 4) ith (X+yt

A:

Q: Evaluate the double integral x2 + 3x + 4y dx dy : y=0 Jx=0 Select one: O 22/3 O 12 O 38/3 O 55/2

A:

Q: Find the expected value of the inf luencer ħ|0 1 |10 For the case represented by the function

A:

Q: F cxrt) Evaluate the probabieity donsity PG) P = 45* 25 e 1 ADe Normalize The wavefunctian to…

A: Given ψx,t= Ae-cm2ℏx2e-i2cmt

Q: The inverse Fourier transform of the position probability amplitude y(x,t) is: a. w(p.t): O b. y…

A:

Q: 3. The ground state and first excited state of the SHO for angular frequency w are Yo (x) = a…

A:

Q: The z-transform of [n] = u[-n] is

A:

Q: II) Find the exponential Fourier transform of the given function I, -T<x<T f(x) = { 0, otherwise,…

A: As given, The function, fx=x,     -π&lt;x&lt;π0,      otherwise   Define the exponential Fourier…

Q: 8. A periodic function is defined as follows: f(t) = { (3 for-1<t <0 for 0 < t < 1 16 i. ii. iii.…

A: We have given a periodic function of time period 2 then we can express by the Fourier series as…

Q: Q# 04: Find Laplace transform of the function 2 Sint

A: The function is of the form tn f(t)  where, n=2

Q: It is impossible within a finite amount of time to add an infinitely- numerous series of terms…

A: