Develop a state space model for a mass m on a smooth horizontal surface

REFER TO THE SCHEMATIC ABOVE WHICH SHOWS THE FORCES ACTING ON THE BLOCK
OF MASS m . THE FORCE Bv IS THE FRICTIONAL FORCE . WE NEGLECT SURFACE
FRICTION IN THIS CASE .WE CONSIDER ONLY AIR FRICTION. X IS THE
DISPLACEMENT FROM THE LIGHT BLUE LINE . THE REFERENCE POINT OF THE
BLOCKIS ON THE LIGHT PURPLE LINE. HERE IS THE EQUATION OF FORCES WHICH
I GOT,

. – eqn1

SO BEFORE DOING THE ACTUAL MODEL OF THE SYSTEM , DO THE FFG . STEPS :

STEP1 --- For part 1 GET eqn1 INTO ITS STATE VARIABLE REPRESENTATION.

STEP2 --- IDENTIFY THE STATE VARIABLE AND DETERMINE ANY RELATIONSHIP
BETWEEN THEM

STEP3 --- IDENTIFY THE INPUTS AS WELL AS THE OUTPUTS YOU ARE INTERESTED
IN .

STEP4 --- SIMULATE THE DYNAMIC BEHAVIOUR OF THE STATE SPACE MODEL USING
SIMULINK – DEVELOP THE MODEL FILE

STEP 5 --- SHOW AS WELL AS PROVIDE written STEPS AS HOW I CAN SIMULATE
THE BEHAVIOUR AND COMMENT ON THE ENERGY TRANSFORMATIONS WITHIN THE
SYSTEM .

STEP 6 --- Modify your model in part 1 above to determine the effect of
dynamically tilting the horizontal surface by an input angle a(t)
relative to the positive x-axis. Note that when this happens the block
will now start to slide down. There the displacement now will be in the
negative direction . We are creating a kind of see-saw effect . So we
have to develop another state –space model for this situation where
the block is on an incline and at an angle a(t) just like in step 1 , 2
and 3 .

Step 7 --- SIMULATE THE DYNAMIC BEHAVIOUR OF THE STATE SPACE MODEL USING
SIMULINK – DEVELOP THE MODEL FILE

Step 8 --- SHOW AS WELL AS PROVIDE written STEPS AS HOW I CAN SIMULATE
THE BEHAVIOUR AND COMMENT ON THE ENERGY TRANSFORMATIONS WITHIN THE
SYSTEM – most importantly ;determine the effect of dynamically tilting
the horizontal surface by an input angle a(t) relative to the positive
x-axis.

STEP9 --- E-MAIL THE SIMULINK FILEs TO MY E-MAIL ADDRESS BELOW :
HYPERLINK "mailto:mwanwarl@mweb.co.za" mwanwarl@mweb.co.za AND SUBMIT
THE REST OF THE SOLNS TO THE WEBSITE

x

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