Consider a mechanical system as shown in figure below.
(i) Construct the free-body diagrams of the system. Properly indicate and label all forces that exist in the system. (NOTE: Answer must be selected from the given choices provided below the figure)
(ii) From the free-body diagrams in (i), by assuming all the unknown parameters (mass, damper and spring) is equal to 1, formulate the transfer function, X2(s)/F(s). (NOTE: Answer must be written in the space given below the figure)
[20 Marks]
[CO2, PO2, C4]
Mechanical system
ANSWER :
(i) Free body diagram of the system. Indicate the direction of the force for each component in the system. choose the direction
| Free Body Diagram On M1 |
Free Body Diagram on M2 |
| f(t) : Answer: <--/--> |
Fk2,x1 : Answer:<--/--> |
| Ffv1,x2 : Answer:<--/--> |
Ffv3,x1 : Answer:<-/---> |
| Ffv2,x2 : Answer:<--/--> |
Ffv1,x1 : Answer: <--/--> |
| Ffv3,x2 : Answer:<--/--> |
Ffv2,x1 : Answer :<--/--> |
| FK2,x2 : Answer: <--/--> |
Fm2,x2 : Answer: -->/<-- |
| Fm1,x1 : Answer-: ->/<-- |
Fk2,x2 : Answer: -->/<-- |
| Fk1,x1 : Answer: -->/<-- |
Ffv3,x2 : Answer; -->/<-- |
| Ffv1,x1 : Answer; -->/<-- |
Ffv1,x2 : Answer; -->/<-- |
| Ffv2,x1 : Answer:-->/<-- |
Ffv2,x2 : Answer;-->/<-- |
| Ffv3,x1 : Answer--><-- |
Fm1,x2 : Answer |
| Fk2,x1 : Answer--><-- |
f(t) : Answer |
(ii) Assume all the value of (mass, damper and spring) is equal to 1.
Laplace value for motion equation on Mass 1
[ ____ s3 + ____ s2 + ___ s + ____ ] X1(s) + [ ____ s3 + _____ s2 + _____ s + ____ ] X2(s) = _______ F(s)
Laplace value for motion equation on Mass 2
[ ____ s3 + ____ s2 + ___ s + ____ ] X1(s) + [ ____ s3 + _____ s2 + _____ s + ____ ] X2(s) = _______ F(s)
X1(s) in function of X2(s)
[ ____ s3 + ____ s2 + ___ s + ____ ] X1(s) = [ ____ s3 + _____ s2 + _____ s + ____ ] X2(s)
Transfer Function X2(s) / F(s)
(es%5E3%2Bfs%5E2%2Bgs%2Bh)%7D%7B(is%5E3%2Bjs%5E2%2Bks%2Bl)%7D%20%24%24)
X2(s) + ![[\ ms^3 + ns^2 + os + p ]\](https://chart.googleapis.com/chart?cht=tx&chf=a,s,000000|bg,s,FFFFFF00&chl=%5B%5C%20ms%5E3%20%2B%20ns%5E2%20%2B%20os%20%2B%20p%20%5D%5C)
X2(s) = F(s)
Fill in the blank below :
a = ____ ; b = ____ ; c = Answer; and d = Answer
e = Answer; f = Answer; g = Answer and h = Answer
i = Answer; j = Answer; k = Answer and l = Answer
m = Answer; n = Answer; o = Answer and p = Answer
Final Transfer Function
If A = and B = , what is the final transfer function in variable A and B. (NOTE: do not put any space in your answer)
%7D%7BF(s)%7D)
= _____________
