The motion of a mass-spring system with damping is governed by y"(t) + 10y'(t) + ky(t) = 0; y(0) = 1, and y'(0) = 0. Find the equation of motion and sketch its graph for k= 23, 25, and 27. What is the equation of motion for k = 23? y(t) = O (Type an exact answer, using radicals as needed.)

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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.