Answer to Question #317528 in Differential Equations for Almas

Question

Applications of Non-Homogeneous Differential Equation

Answer 1

Applications of Nonhomogeneous Differential Equations

Non-homogeneous second order differential equations have broad applications in engineering analysis.

The second-order nonhomogeneous differential equations are employed in predicting the amplitudes of vibrating mass in the situation of near-resonant vibration and the physical consequences to the mass-spring systems.

Thus, Non-homogeneous differential equations have:

(1) Applications in forced vibration analysis.

(2) Application in “resonant vibration Analysis” of solid machine structures that often results in devastating structural failures, and

(3) Application in “near resonant vibration analysis.” This type of vibration usually takes long time for structural failure. But structural failure is mainly caused by the “fatigue” of the materials.