On the Moodle site just below the assignment you will find data from a slow sine sweep test conducted on a car on a "four-post" road simulator for the frequency range 0 to 20 Hz in the EXCEL spreadsheet "Ride_Comfort_Data".   The response has been measured vertically on the seat rail of the driver's seat while the front two actuators moved up and down in phase and the rear actuators remained at rest.  The amplitude of the actuator motion was such that the velocity amplitude was constant throughout the frequency sweep at 100 mm/s.  The response amplitude at the seat rail is measured in g.

(a)  Obtain the transmissibility between the input motion of the actuators as a single input and the motion of the seat rail.  Provide a graph from EXCEL showing the transmissibility.

(b)  The transmissibility in (a) does not tend to 1 at low frequency as might be expected for an ideal one degree of freedom system.  Explain this.

(c)  Estimate the natural frequency and damping factor for the sprung mass mode involving motion of the body on the front suspension.

(d) If the diameter of the front tyres of the car is 0.6 m estimate the car speed in kph which would cause an "engine shake" problem in the car.  (This will require you to identify the frequency for the engine shake mode from your graph.)                                           

(e)  In road tests on a relatively flat test track surface at 80 kph with one front wheel deliberately unbalanced, the idle shake at the seat rail position, measured using an accelerometer, was 4.2 g rms.  The other three wheels were in almost perfect balance.  What displacement amplitude and frequency of the front two actuators of the road simulator would be necessary to achieve the same seat rail motion in the laboratory?