matlab and simulink 12 labs and every lab 4 questions

Tutorials No 7

All working and MATLAB programs to be kept/typed up in Microsoft

Word, which would be submitted on 31/03/2017

Use MATLAB to help answer the following:

(1) A mass of 15kg is connected to a vertical wall by a spring of stiffness

1800kgs -2

and a damper of damping constant 52.58kgs -1

(the mass can be assumed

to be mounted on air bearing which are perfectly frictionless). Initially the system is at

rest, with the distance between the mass and the wall equal to 0.42m. A horizontal

force of 250N is suddenly applied to the mass (in the direction of the wall)

(i) What is the magnitude of the first ‘overshoot’ of the mass and what is the

magnitude of the first ‘undershoot’?

(ii) What is the final distance of the mass from its initial position? How could this

have been determined without plotting ‘displacement versus time’ using

MATLAB?

(iii) What is the damping ratio?

(iv) What is the closest that the mass comes to the wall?

(v) What is the period T of the decaying oscillation of the mass? How does this

period T compare with the period associated with the undamped natural

frequency, ?

(2) A mass of 200kg is suddenly placed onto a car roof. In response, the car

drops to a maximum distance below its initial position, rebounds (first

undershoot) and then oscillates before settling down to its final position. It is

noticed that at the first undershoot the car is 0.0621m from its initial position.

The mass of the car is 1500kg, its overall spring stiffness is 28210kg/s 2

and its

overall damping constant is 4163.2kg/s.

(i) What is the maximum distance of the car body below its initial position

(ii) What is the final distance of the car body below its initial position

(iii) What is the oscillation frequency in Hz of the car body while it is

oscillating?