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A bump profile has been provided, which provides a vertical displacement over time for one wheel, based on the profile shown. It is suggested that you use a quarter-car model initially, in order to familiarise yourself with this system before proceeding to the half-car model.
2.  Create a half-car model in Simscape Multibody with the given parameters, using joints which appropriately allow motion. .
3. Identify a location on the car body where the drivers head is likely to be and use this as a point from which to measure driver acceleration and displacement (use a transform and a transform sensor).
4. model output:
Driver displacement (absolute and relative to car), driver upward acceleration (absolute),
Tyre displacement (compression)
Force at suspension mounting (top)
5. Evaluate  the  sensitivity  of  the  response,  in  terms  of  acceleration  and  displacement experienced by the driver, to TWO OF THE LISTED PARAMETERS AS ALLOCATED TO YOU over the required range of speeds.
6. Investigate the sensitivity of the model to change of solution algorithm (use a single instance from your models above (i.e. one velocity, one set of parameters) and run with a range of algorithms. Consider the effect of step-size also. Be sure to look at acceleration as well as position in your analysis.
7. Develop a set of lagrangian dynamics equations for the quarter-car model, subjected to a vertical force applied to the body, and solve these using one of the matlab solvers such as ode45, comparing your results with your simscape multibody quarter-car model for one set of parameters.
8.  The following will attract extra credit:
a.    Implement a separate body to represent the driver on a suitably sprung seat and compare the effect on this separate driver with your earlier results for each scenario.
b.  Car dampers often have a different damping constant for the bump and return. Find a way to implement this logic.

vehicle dynamics- modeling with matlab simulink
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