I will give full rating if all parts of this question areanswered correctly with work shown in each step. THANK YOU!!
Imagine now that you are driving on a dirt washboard road in the desert. Assume that the road has a sinusoidal shape with amplitude A = 5 cm and period L = 20 pi cm (this is the distance between two consecutive bumps). At speed s, the automobile will complete a cycle on the road in time L / s, therefore, the relative height of the road beneath the wheel can be modeled by h(t) = Asm omega t, where omega = 2 pi s / L. The mass (the car) moves up and down in response to the height of the road it is traversing. Using Newton's second law, the height (bounce) of the car with respect to the equilibrium position will be given by the equation: my" = - k(y - h) - c(y'-h'), where k is the spring constant, and c is the damping constant. Show that the equation above is equivalent to my" + cy' + ky = Ak sin omega t + Ac omega cos omega t. Consider the mass of the car to be m = 1000kg, c = 40000 kg/s. k = 2.9 106 N/m. Kind the speed s of the car at which resonance occurs. Find y(t), assuming ,y(0) = 0, y'(0) = 0, and graph the solution. 4. What is the steady-state amplitude of the car's motion at resonance? You decided that you can't take the bouncing anymore, and you double your speed s. What is the steady state amplitude now? What is it if you triple your speed? Graph y(t) in these two cases, at the same scale as the graph from part 4. While you are driving at triple the resonance speed, you don't notice that a pothole 0.5m wide is ahead of you. Are you going to be able to "fly" over it? Assume that if don't lose more than 1 cm in height while you are airborne, you will be able to land on the other side, Take g = 10m/s2.
