This paper concentrates on the primary theme of Assuming that u(x,t) can be separated into a function of space x multiplied by a function of time t, show that the system is represented by two Ordinary Diﬀerential Equations in which you have to explain and evaluate its intricate aspects in detail. In addition to this, this paper has been reviewed and purchased by most of the students hence; it has been rated 4.8 points on the scale of 5 points. Besides, the price of this paper starts from £ 40. For more details and full access to the paper, please refer to the site.
Assuming that u(x,t) can be separated into a function of space x multiplied by a function of time t, show that the system is represented by two Ordinary Diﬀerential Equations (ODEs). State these equations, the two boundary conditions, and the two initial conditions that are necessary to solve for a unique solution. (8%)
2. Apply the boundary conditions to solve the spatial ODE. State the general solution to the time ODE. Then determine an expression for the displacement u(x,t) in terms of wave-speed, c, and the Fourier coeﬃcients. (5%)
3. After some lab testing, you discover that an initial velocity proﬁle shown in Equation 2 causes the web to vibrate continuously at a frequency of f3 = 540 Hz and that the wave-shape is exactly a 3rd mode sine wave with amplitude A = 1.0 × 10−3m. Use this information to determine the wave-speed, c, and state clearly the eigenvalues/eigenfunctions of the system. Hence present the complete analytic solution for this problem. (7%)