Please show and explain all hand written calculations. Show equations and steps.

Post the MatLab code

1. A simplified model of the suspension of a car consists of a mass, m, a spring with stiffness k, and a dashpot with damping coefficient c, as shown in the figure. A bumpy road can be mod- eled by a sinusoidal up-and-down motion of the wheel = Ysin (cor). From the solution of the equation of motion for this model, the steady-state up-and-down motion of the car (mass) is given by x=Xsin(or-4). The ratio between ampli- tude X and amplitude Y is given by: mco3 k(k-mo2) (oc) Assuming that m- 2000 kg, k-500 KNm. and c = 38 X 103 Ns/m. determine and plot the variation in frequency, o, for values of 0.1 s X/Y S 1 in increments of 0.05 using a MATLAB M-file written by you y= Ysin (or) Thoroughly discuss the effect of XY on the frequency o. Does youi conclusion change if c is doubled or halved? 1. A simplified model of the suspension of a car consists of a mass, m, a spring with stiffness k, and a dashpot with damping coefficient c, as shown in the figure. A bumpy road can be mod- eled by a sinusoidal up-and-down motion of the wheel = Ysin (cor). From the solution of the equation of motion for this model, the steady-state up-and-down motion of the car (mass) is given by x=Xsin(or-4). The ratio between ampli- tude X and amplitude Y is given by: mco3 k(k-mo2) (oc) Assuming that m- 2000 kg, k-500 KNm. and c = 38 X 103 Ns/m. determine and plot the variation in frequency, o, for values of 0.1 s X/Y S 1 in increments of 0.05 using a MATLAB M-file written by you y= Ysin (or) Thoroughly discuss the effect of XY on the frequency o. Does youi conclusion change if c is doubled or halved