6. 10 pts Use Laplace transforms to solve the damped spring-mass system xi’ +3×1 +2x = 0; x(0) = 1, 40) = —1.

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5. a) find the Laplace transform of f(t)= { 21 1 < 3; , > 3. b) Find the inverse Laplace transform of F(s)== (s+V-i-4*

4. (a) [10 pt] Solve without Laplace transforms: y” —2y’ +5y = 0; y(0) = 1, y'(0) = 5. (b) 110 pt] Find the general solution of y” +4/ = 10ex.

3. Consider the differential equation —da = f(x) where f has the graph shown. dr (a) 15 pc) Determine the equilibrium solutions. (b) [5 pt] Which solutions in (a) are stable and which are unstable? (c) [5 ptj Sketch the ...

2. Solve the following equations explicitly for y(x). (a) [10 pt] y’ + 2y = e (b) [10 pt] .x-y’ = _x-y2 + y. Hint. Bernoulli.

1 As a body body cools by radiation its temperature T at time k is a positive constant. t satisfies the equation — dT = _ k 7- 4 where (a) (lOpt1 Find a general solution of the differential equation. ...

4 in a wireless cellular system, let’s consider a cell with radius of 50Km” with /EIRP (Effective isotropic radiated Power) or 16w. The cos or blocking probability “. is 3%. Assume that average call length (1/u) Is 10 minutes. and ...

3. This problem 1s on the free space path lose between a transmitter and a receiver separated by the distance d [Km]. Let’s assume that transmit power Pi- 20 antenna gain Gr. 10 db and Rx antenna gain G.- 20 ...

2. This problem is on the instantaneous Code and Huffman code. (n) For the 6- symbol source with probabilities 0.35, 0.25, 0.2, 0.1, 0.05 and 0.05, give Huffman Ternary Code and its Average length.(show Table) (6) (b) Which of the following code(s) ...

1. Assume that the received signal at the receiver antenna of the mobile is defined as r(0= 10 + 2 e Ham +3 efts) (a) Calculate the received signal envelope R CX24-Y2, where X denotes the real part and Y refers ...