Complex Variables and Partial Differential Equations (3130005)

Modeling and solution of the Wave equations

BE | Semester3 Topic : Modeling and solution of the Wave equations

Q5 (c) Winter-2019
A string of length $L = π$ has its ends fixed at $x = 0$ and $x = π$ . At time $t = 0$ , the string is given a slope defined by $f (x) = 50 x (π - x)$ , then it is released. Find the deflection of the string at any time $t$ .

7 Marks

Unit : HIgher order partial differential equations and applications

Q5 (c) Winter-2019
Derive the one dimensional wave equation that governs small vibration of an elastic string. Also state physical assumptions that you make for the system.

7 Marks

Unit : HIgher order partial differential equations and applications

Q5 (c) Summer-2020
Find the solution of wave equation $u_{tt} = c^{2} u_{xx}, 0 \leq x \leq π$ with initial and boundary condition $u (0, t) = u (π, t) = 0; t > 0, u (x, 0) = k (\sin x - \sin 2 x), u_{t} (x, 0) = 0; 0 \leq x \leq π, (c^{2} = 1)$

7 Marks

Unit : HIgher order partial differential equations and applications