A spring/mass/dashpot system has mass 1 kg, damping constant 7 kg/sec and spring constant 12 kg...

  

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A spring/mass/dashpot system has mass 1 kg, damping constant 7 kg/sec and spring constant 12 kg per sq sec. The system starts at rest and then has an external force of e2 Newtons applied after t seconds. The IVP below models the system: "+7z'+12z e 2, 2(0)=0, z'(0) = 0 The Laplace transform of the IVP has solution X(s) = F(s) (s) where F(s) represents the Laplace transform of the forcing term e 2t and (s) represents the transfer function. (8)= The weight function w(t) is the inverse Laplace transform of the transfer function. w(t) L (b(s)) The solution to the IVP is the convolution of the forcing term with the weight function. f(t)*w(t) A spring/mass/dashpot system has mass 1 kg, damping constant 7 kg/sec and spring constant 12 kg per sq sec. The system starts at rest and then has an external force of e2 Newtons applied after t seconds. The IVP below models the system: "+7z'+12z e 2, 2(0)=0, z'(0) = 0 The Laplace transform of the IVP has solution X(s) = F(s) (s) where F(s) represents the Laplace transform of the forcing term e 2t and (s) represents the transfer function. (8)= The weight function w(t) is the inverse Laplace transform of the transfer function. w(t) L (b(s)) The solution to the IVP is the convolution of the forcing term with the weight function. f(t)*w(t)