The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads to the differential equation mx´´ + kx = F0 cos(ωt), where m is the mass of the object attached to the spring of constant k. Suppose the mass of the body is 1 kg, the spring constant is 9 N/m, the amplitude of the external force  F0 is 80 N, and the frequency ω is 5 rad/s . Obtain the equation of the position of the mass (with respect to time) if x(0)=x´(0)=0

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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.