9. Two coupled quantities, displacement S and velocity V, are related through the system: ds = v, dt dv = -3 s – 4v dt Calculate the general solutions for the displacement S and velocity V as...

Extracted text: 9. Two coupled quantities, displacement S and velocity V, are related through the system: ds = v, dt dv = -3 s – 4v dt Calculate the general solutions for the displacement S and velocity V as functions of time by solving this system using eigenvalues and eigenvectors. A cubical tank (sides 2 meters) is filled with water to height 10. 0.2 m d H = -0. 03 dt H(0) = 1.3 Hn+1 = Hn+ h f(H„) +, f'(H,) h? using the Taylor method of order 2 Use the step size h = 0.2 and recurse twice to generate H(0. 2) and H(0.4) H = 1.3 m at t= 0 The water is drained through a circular hole with diameter . Solve the first degree differential equation Use five decimal point accuracy.