show work by hand

For this problem, you will determine the response y(t) of the quarter-car model shown below driving over a bump described by u(t). The dynamics of the quarter-car model are given by my(t)+by(t)+ky(t)=bu(t)+ku(t) where m is a quarter of the mass of the car chassis, k is the suspension stiffness, and b is the suspension damping. The input u(t) is the road height. The numerical values of the parameters are m=1,b=6, and k=10. a) Find the transfer function G(s) from U(s) to Y(s). b) Find the Laplace transform U(s) of the input u(t) above. - compute U(s) using only properties from Tables 2.1 and 2.2 in your book. c) Compute the output response Y(s)=G(s)U(s) in the frequency domain. - If you were unable to complete part (b) then compute the step-response Y(s)=G(s)1(s) for partial credit where 1(t) is a step-function. d) Use partial fraction expansion to convert Y(s) into time-domain y(t). - If you were unable to complete part (b) then compute the step-response y(t)=L1[G(s)1(s)] for partial credit. e) Use MATLAB to plot the response y(t). - HINT: Use MATLAB function impulse with G(s)U(s)