Consider the differential equation dz dz m dt2 +p, + kz = F(t) dt which models an oscillator of mass m subject to a restoring force k, damping p and an external force F(t). The external force F(t) is given by F(t) = 18e-* and also m = 1, p = 4 and dz k = 13. Initial conditions are that z = 1 and = 4 when t = 0. dt (i) By taking the Laplace Transform of the differential equation show that 7, (the Laplace Transform of the solution) satisfies s2 + 10s + 34 (s + 2)(s² + 4s + 13) (ii) Hence find z(t). post (iii) Explain what happens to z(t) for large t.

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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.