Using condition (iv) in the above equation, we get, A tightly stretched string with fixed end points x = 0 & x = ℓ is initially at rest in its equilibrium position . Laws and engineering principles and systems are in the final week, differential! T(t) be the solution of (1), where „X‟ is a function of „x‟ alone and „T‟ is a function of „t‟ alone. (10) A rectangular plate with insulated surface is 10 cm. Find the displacement y(x,t) in the form of Fourier series. Differential equations are used to calculate how intense the water will flood at the front thinking the speed that water drains out of the culvert and the speed that water flows into the … several variables and partial derivatives). Since we are dealing with problems on vibrations of strings, „y‟ must be a periodic function of „x‟ and „t‟. long, with insulated sides has its ends kept at 0o C and 100o C until steady state condition prevail. long have their temperatures kept at 20, C, until steady–state conditions prevail. Y(y) be the solution of (1), where „X‟ is a function of „x‟ alone and „Y‟ is  a function of „y‟ alone. It is set vibrating by giving to each of its points a  velocity   ¶y/¶t = g(x) at t = 0 . Differential Equations are extremely helpful to solve complex mathematical problems in almost every domain of Engineering, Science and Mathematics. A rod of length „ℓ‟ has its ends A and B kept at 0°C and 100°C until steady state   conditions prevails. fastened at both ends is displaced from its position of equilibrium, by imparting to each of its points an initial velocity given by. (3) Find the solution of the wave equation, corresponding to the triangular initial deflection f(x ) = (2k/ ℓ)   x   where 0
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