5. The motion of a mass attached to a dashpot and a spring as it experiences a force can be represented by dx d?x Fr = -kx Fg = -B- dt Fm = m dt2 As the net force (F) is equal to 1, the following differential equation can be written: FB + Fm + Fx = 1 d?x dx m dt2 -B- kx = 1 dt Where m = 1, B = 1 and k = 6, Solve the above differential equation using the Laplace Transform method at the following initial conditions, x(0) = 0, x'(0) = 0. %3!

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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.