A spring/mass/dashpot system has mass 1 kg, damping constant 5 kg/sec and spring constant 6 kg per sq ot sec. The system

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A Spring Mass Dashpot System Has Mass 1 Kg Damping Constant 5 Kg Sec And Spring Constant 6 Kg Per Sq Ot Sec The System 1 (25.33 KiB) Viewed 27 times

A spring/mass/dashpot system has mass 1 kg, damping constant 5 kg/sec and spring constant 6 kg per sq ot sec. The system starts at rest and then has an external force of e Newtons applied after t seconds. The IVP below models the system: x” + 5x' + 6x = e−6, x(0) = 0, x'(0) = 0 The Laplace transform of the IVP has solution X(s) = F(s) (s) where F(s) represents the Laplace 6t transform of the forcing term eft and (s) represents the transfer function. $(s) = The weight function w(t) is the inverse Laplace transform of the transfer function. w(t) = L ¹(Þ(s)) = = The solution to the IVP is the convolution of the forcing term with the weight function. f(t)*w(t) =