SATTPrevious years University Questions From UNIT 2

TOPIC : Laplace TransformJAN 2015(SUPPLY)1. Obtain the Laplace transform of sinwot u(t) (2 ½)

2. Find inverse I.L.T. of X(S) = S

S2+a2 (2 ½)

3 . Use Laplace transform technique to find step response at t = 1, y(t) of a system initially

relaxed if it is described by dydx

+0.9dydx

+0.2 y=x (t) (10)

JUNE – 2014 (MAINS)1. Find the Transfer function and Step response of the following System (5)

2. Find The Laplace Transform and ROC of the signal x(t) = 2e-3tu(t) + 4e5tu(-t) (2 ½)3. Find the Initial and Final value of the signal x(t) whose Laplace transform is

X(S) = 10

S2+8S+15 ; Re(S) > -3 (2 ½)

4. Find the Laplace transform of x(t) = 5te-3t Cos5t U(t) (5)

5. State and Prove FVT for LT and Find the Final value of x(t) whose L.T is X(S) = 10

S2+5S (5)

APR 2013(MAIN)1. Find the L.T of x(t) = e−atU(-t) (2)2. Consider a CT system with I/p and O/p relation Find (a) the System function (b) Determine the Impulse response for each of the following cases (i) the System is Causal (ii) The sytem is causal and stable (10) DEC 2013(SUPPLY)

1. Find the ILT of the following function X(S) = S+5

S2+6S+25(4)

2. The transfer function of a CTS is given by H(S) = 5

S (S+5) . Find the Impulse reponse of the

System. (2)JAN 2013 (NEW) (SUPPLY)1. Find the L.T of a unity. (2)

2. If X(S) = S2+6S+7S2+3S+2

Re(S) > -1 is the L.T of x(t) Obtain the ILT , x(t)

(4)JUNE 2012 (MAINS)1. (a) Find the response of the system described by the differential EQN Where x(t) = e-2tu(t) (10)

(b)Find the Impulse response of the system h(t)2. A certain signal has L.T but does not has F.T . Is it true.Justify your answer (2 ½)

3. What is the ILT of X(S) = 3

(S+1)2+22 ( 2 ½)

4. Solve the following Integral using L.T (5)5. State and prove Integral property of L.T (5)

JUNE 2012(NEW) (MAINS)1. Find the transfer function of the continuous LTI causal system described by the following Differential EQN (2)

2. Find Initial and final value of the signal whose L.T is given by X(S) = 4

S (S+1)2 , Re(s) > -1

(4)JAN-2012(SUPPLY)1.What is the L.T of e-3t[u(t) – u(t-4)] (2 ½)2. What is the significance of ROC. (2 ½)3. Find the L.T of a) 5u(t)u(3-t) b) e-3t[u(t+2) – u(t-3)] (10)

4. Find the ILT of a) F(S) = e−2S

(S+1)(S+2)2 b) 1−e−3 S

3S3+2S2

(10)

JAN-2011(SUPPLY)1. Find the L.T and its associated ROC for the signal x(t) = δ(at +b) , a & b are constants ( 2 ½)

2. Find the ILT for X(S) = 2S+1S+2

Re(s) > -2 (2 ½)

3. State and prove time scaling property of L.T (5)4. Obtain the L.T of x(t) = e−atCosw0t u(t) (5)June-2011(Main)1. State and prove scaling property of L.T (4)

2. If the L.T of x(t) is X(S) = 4

(S+2)2 Find the L.T of g(t) = x(2t – 2)

(6)

3. Find the ILT of X(S) = 4(S+1)S2+2S+2

(5)

4. The transfer fn of a system is H(S) = S+2

(S+3 )(S+4)2 .Sketch the Pole – Zero Plot and Test

The stability (5)JUNE – 2010 (MAIN)1. Find the L.T of x(t) = e-2t[u(t) – u(t-5)] ( 2 ½)

2. Find the ILT for X(S) = 2S+4

S2+4 S+3( 2 ½)

3. Find the L.T of x(t) = (e-tCos2t -5e-2t)u(t) + 12

e-2tu(-t) (5)

4. Find the ILT of X(S) = Ss+2S+5

(S+3 )(S+5)2 Re(S) > -3

(5)APRIL – 20091. Find the L.T of f(t) = Cos w(t-t0) (2 ½)2. Obtain the L.T of f(t) = Cos2wt ( 5)

3. Obtain the ILT of F(S) = 5

S2 (S+1 )(S+2)2 (5)

DEC 2009

1. Find the ILT of F(S) = e2S−e3S

S2+2S+2(5)

2. Find the L.T of f(t) = te-atu(t) ( 2 ½)APR 2008 (NEW) (MAINS)

1. Find the ILT of X(S) = S2

(S+a)2 (2 ½)

2. State and Prove Convolution theorem (5)

3. Find the convolution of the functions whose L.T are F1(s) = 1S

and F2(s) = 1

(S+1) (5)

DEC 2008 (SUPPLY)1. Find the L.T of an Impulse function (2 ½)2. If the T.F of the system is H(S) = 1/(S+3) .Find the response with e-2t as I/P (2 ½)3. Obtain the L.T of f(t) = te-atSinwt (5)

4. Obtain the ILT of F(S) = S2

(S2+1)2 (5)

5. An LTI system is described by the following EQN .Find the Impulse response (5)

APR-2007 (MAINS)1. Consider the signal x(t) = e−5 tu(t) + e−βtu(t) . Denote its L.T by X(S) . What are the constraints placed on real and imaginary parts of β if the ROCnof X(S) is Re(S) = -3 (5)2. Find the L.T of x(t) = e tSin2t t ≤ 0 = 0 else (5) Indicate the location of its polesDEC-2007(SUPPLY)1. State and Prove time differentiation property of L.T ( 2 ½)

2. Find the ILT of 1

(S+a)2(2 ½)