A second order differential equation involves the unknown function y, its derivatives y' and y'', and the variable x. Second-order linear differential equations are employed to model a number of processes in physics. Application of Second Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering San Jose State University San Jose, California, USA ME 130 Applied Engineering Analysis. The general solution to the ode is thus x(t) = c1e2t+c2e3t. With the model just described, the motion of the mass continues indefinitely. Applications of Second‐Order Equations. Application Of Second Order Differential Equation. Use of the initial conditions then results in two equations for the two unknown constant c1and c2, c1+c2= 2, 2c13c2= 3, with solution c1= 9 and c2= 7. Damped Vibrations. The solution for x˙ obtained by differentiation is x˙(t) = 2c1e2t3c2e3t. Therefore, the position function s ( t) for a moving object can be determined … … Theory and techniques for solving differential equations are then applied to solve practical engineering problems. Chapter Outlines The principal quantities used to describe the motion of an object are position ( s ), velocity ( v ), and acceleration ( a ). Detailed step-by-step analysis is presented to model the engineering problems using differential equa tions from physical principles and to solve the differential equations using the easiest possible method. Skydiving. Since velocity is the time derivative of the position, and acceleration is the time derivative of the velocity, acceleration is the second time derivative of the position. applications.