A 16-lb weight stretches a spring 4 ft. This spring–mass system is in a medium with a damping constant of 4.5 lb-sec/ ft, and an external force given by ƒ(t) = 4 + e^-2t (in pounds) is being applied. What is the solution function describing the position of the mass at any time if the mass is released from 2 ft below the equi-librium position with an initial velocity of 4 ft /sec downward?

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A: Solution :

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.