Examples of Governing Differential Equations, Boundary Conditions, Initial Conditions, and Exact Solutions for Some Engineering Problems ТАBLE 18.8 Governing Equation, Boundary Conditions or Initial Conditions Problem Type Solution Example 1: The deflection of a beam. wX(L – X) Deflection of the bearn Y, as the El- function of distance X: 2 Boundary conditions: at X = 0, Y - 0 and at X = L, Y – 0 X4 + 2LX – EX) 24EI E,I Example 3: The temperature distribu- tion along a long fin. hp dX? kA Temperature distribution along the fin as the function of X: (T-T) = 0 Example 2: The oscillation of an elastic d' y +wy – o dt? The position of the mass y, as the function of time: y(t)= y, cos le,? system. k where w? = undary conditions: at X - 0,T-e T = T„+(Tose-Tu )e Tair, h Tpase as L- o,T = T. Initial conditions: at time t = 0, Yo y = y, and at time t = 0,0y = 0 dt P = Perimeter

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Engineering Mechanics- II (Dynamics) Ind. Assignment- 1 1. The velocity of a particle is given by v = 25t² - 80t - 200, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration versus time for the first 6 seconds of motion and evaluate the velocity when acceleration is zero.

Euler Cauch equation is used to solve * Non linear differential equation Linear differential equation O Linear and non linear differential equation O Homogenous differential equation Non of the above