Task:

Section A

1) Implement a Simulink model of the above equation and, assuming that it is possible to step change the applied force by instantaneously adding the mass M, at time t = 0, evaluate its step response.

2) Derive the transfer function equivalent to the differential equation given and expand your Simulink model of A1 above to demonstrate that it is correct.

3) What error would you expect to see if the initial conditions for x in the simulation for A1 were not zero when attempting A2 and how could you resolve it within Simulink ?

Section B

The response obtained in A1 above should be of the form, x = Asin(t + ) , where A,  and are constants.

1) From your response of A1 demonstrate how the Simulink Sine Wave Function block shown opposite can be used to replicate your results.

2) Use Simulink to construct the equation for x and demonstrate its equivalence to the Sine Wave Function block.

3) Perform research, or use your simulation, to determine how the settings  derived in B1 above relate to the constants M and KS.

Section C

1) In practice a continuous oscillation will not occur and the oscillationsamplitude will exponentially decays with time due to damping.

Re-develop the differential equation given to allow for constant damping (with a damping coefficient b Kg/s ).

2) An experiment was performed on your system and it was recorded that the oscillations decayed exponentially with a time constant, , of 10 seconds.

Construct the Simulink model of the damped system and use it to evaluate the value of damping present in the expriment.

You may assume that the decay amplitude is expressed via Ae  t t   sin 

3) Explain the physical reasons for the presence of damping in a real system.