Answer Happy

1 m This project is to solve a differential equation that models a shock ab- sorber of a car using the 4th order Runge-Kutta method implemented as a Matlab script for which you can use the free software Octave as described in lectures or CPUT licensed Matlab. The model is taken from https://steemit.com/steemstem/(masterwu/ modelling-car-suspension-with-second-order-ode-3-damped-free-oscillations The differential equation derived there with simplifying assumptions to model 1 shock absorber of a car is e dy k (1) m dt Where: 1. y is the vertical displacement of the shock absorber 2. t is the time 3. m is a quarter the mass of the vehicle m = 350kg + num3kg 4. k is the spring constant k = 1200N/m 5. c is the damping constant c = 600N s/m initially but you should vary it as described below num3 is the last 3 digits of your student number Use a starting value for the damping constant of 600N s/m as in the reference but vary the coefficient so that you have 2 oscillations of your system before the oscillation is damped out. 1
Take y(0) = 0.15m and in initial velocity of shock absorber, 0. at t = 0 as in the reference. Find a suitable time step for your Runge- Kutta implementation by comparing the answer to the solution given in the reference. 1. Once you have found the damping coefficient add trapezoidal integra- tion to your code to find the integral of the function that you have only as a set of points. Also say what this integral represents in your report. 2. you should submit a report descriping your work including documenting your Matlab code, the theory for your numerical methods, your starting parameters and process for varying parameters to find the solution that meets the specifications and the final results. 3. Your report (word or pdf) should have an Introduction section, Theory section, Numerical Results section and Conclusion and the code in an Appendix 4. Your results section should include a plot of the function values and you should discuss the plot (graph) in the accompaning text. In gen- eral all figures presented need to be explained in the text (for all re- ports/theses)