University of Mumbai 2008-3rd Sem M.E Mechanical Engineering System Modelling & Analysis - - Question Paper
X,{s)
F(S)
10
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and X,(i) |
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[to) Find the Transfer functions
where,
K,
C,
C*
Cs
2 N-s/m
1 N-s/m
2 N-s/m
M,
M.
2 kg
3 kg.
2 N/m
K2 = 3 N/m
(Jj L/ff.w neat bKUicntfb wfitiiitjvwi Jicgeasdf y.
(4) Figures to the right indicate full marks.
(5) Asuume suitable data, If neceaaary, A . ii A~. /aJaj
eTrr\) <AlL<XAn QL (TV<~ St\/)Uaaa Mwu>M 9 f \
(a) lixpfaln pointwise, with the help ot a field problem, "Dynamic System Modeling and Analysis". | Q
X2(s)
F(s)
Define : Dynamic System, Lumped or Discrete System, Linear Time Invariant Model.
(a)
(*)
(c)
Find L1 { - }
\s(s + 1) j
using; {) Integration Theorem
(ii) Partial Fraction Method
(iii) Convolution Metnod,
The governing equation for a mechanical system is *x + 2x + x m f(t), where x represents the displacement and I the applied force. Initial conditions are x(0) * O'and x(0) 2. Assuming the applied force is a unit-step function (ind the response. Decide whether Final Value Theorem applies to X(s). If so, find the final value of x(t).
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(h) Consider a complex lime function as shown below : |
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(b)
10
(*
(c>
10
4
fa)
(O)
Express f(t) as a linear combination of step functions and therefrom determine its Laplace Transform. Confirm your answer from Lapiace transform taken directly.
Find nut the tima response for tindardampad vibrations of a spring-mass-damper system where initial conditions for displacement and velocity are zero and excitation force is constant. Use L.T. method only Interprete the answer.
OR
Write a note on Dynamic Modelling [Mathematical) of liquid level systems having two tanks In series.
Relate various parameters of a mechanical system to analogous electrical system using voftage-force analogy. Name the law governing each system.
Find aqutvaltnl spring constant in case of springs working in parallel and In series.
Tabu/ate for fl-L-C circuit, the relationships between voltage-current, currenl-voitage, toftage-cftarge and write Impedance and Admittance for each of the passive element. Write tfte units consistent for various terms.
(C)
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Write the Mesh equations and find transfer function . XH V(s) |
 |
10
yuM
Systems. Writs the consistent units for various terms Involved.
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Find transfer function for the gear train shown below. Transfer function G(5)=-?~ * (*) N i |
 |
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J, = Z kgm2 Ja * 4 kgm2 60 N-m/rad 8 kg-m2 04 * 20 N-m-s/rad |
Ja
Analyses tor time response of temperature of a metal block suddenly placed in hot liquid bath of constant temperature Jm.
6. (a>
Determine temperature constant.
Substitute the following values on the final derivation to gat the tlrfte constant.
Block : sphere
Diameter: 9 cms
Density.- 9000 kg/m3
Specific heat * 0-4 kJ/kg, *C
Thermal conductivity 380 W/m, "C
ConvecUve Heat Transfar Co-efficient 25 W/ma, C.
Is it valid to use lumped parameter model ? Justify.
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02(s) tor the electromechanical system shown below | |
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Tmrqtu |
(b) Find transfer function G(s)
12
2 kg-m2
4 kg-m2 4 kg-m2 16 kg-m2 1 kg-m*
10
20
10
20
C4 * 8 N-m-s/rad .) -
|a)
(b)
7.
(c)
10
Compare state space approach with T.F. approach In the modelling of Dynamic Systems. Define :
State of Dynamic System State variable State-space State eqjations Output equation.
Obtain state space Representation for the system shown below :
u{t) - external force applied to mass m2. y; z are the outputs measured from the respective equilibrium positions.
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Attachment: |
| Earning: Approval pending. |
