- B Consider The Differential Equation P2 P M Kz F T Dt Dt Which Models An Oscillator Of Mass M Subject To A Res 1 (37.1 KiB) Viewed 69 times
(b) Consider the differential equation P2 + P m + kz = F(t) dt? 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-24 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 z, (the Laplace Transform of the solution) satisfies 82 + 10s +34 (s + 2)(s? + 4s +13) Post (ii) Hence find z(t). (iii) Explain what happens to z(t) for large t. wars]