Homework/ For a normalized wave function (x) = Asin (TX), verify the normalization constant A for n = 1 and L= 1nm. 11
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- 5. Sketch the following function in frequency domain plot: i. Y(t) = 3 sin (4лt) + 4 cos (4 лt) ii. Y(t) = 12 sin (10nt) + 5 sin (20лt) + sin (100лt)QUESTION 8 A string is fixed on the x-axis at x = 0 and x 3. The displacement U(x,t) for the vibrating string at any time t satisfies the wave equation ôx? at? and initial conditions U(x,0) = 2 and (x,0) = 0. Find U(x,t) which satisfies the boundary %3D at value problem.Question 3 a) Consider the system shown in Figure Q3a, consisting of a spring connected to the free end of a clamped bar. Estimate the first two natural frequencies using finite element approach. The element matrices are given by [M]=P\[1 PA2 1] 1 2 and [K] spring k E, P Figure Q3a. b) Describe the convergence studies that are carried out during a finite element based modal analysis. c) Describe mode shape orthogonality. Use mode shape vector, mass and stiffness matrices in the discussion.
- The integrals arise when finding the Fourier series expansion of eax over the interval -L< x < L. Use the result cosnл = (-1)" for integral values of n to establish the stated result. eax sin nxdx = (−1) n+1 (eaл. Lea e -ал for integral (a² + n²) values of n.Q5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.3. Calculate and solve the characteristic equation for the following system: (t) -1 | (t) 0 [ 8 ] *) + 10 [ 17 ] x ) = ( [1] -1