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Problem  Derive the transfer functions )((s )((s)  ) and from the given block diagram: R(s) s)  R(s) +  Problem 2 Draw a block diagram for the following equation

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Problem 
Derive the transfer functions )((s )((s)  ) and from the given block diagram: R(s) s) 
R(s) + 

Problem 2 Draw a block diagram for the following equation. The output is X(s), and the inputs are F(s) and G(s): 
+ + 7x = 1 0 f(t)— 4g(t)+ f(t) Make sure that your block diagram is MODULAR; block diagram with a single block that contains a long transfer function does not eam any points. 
Problem 3 Dynamic system is modeled with the following transfer function: Y(s) 8  F(s) 3s3 + 4s + 6 Reconstruct the governing equation from the given transfer function, and derive the state-space model considering that system input is f(i) and system output is AO+ 2.110+-1.(t). 

PART 1 — Method of Undetermined Coefficients Solve the following problems with Method of Undetermined Coefficients Problem I .V(t)+8±(t ) 6x( t) = 2te 4r Problem 2 A(i)±2(t)± 2x(f)=10sin(f), x(0)=0, .(0)=3 PART II — Laplace Transform Solve the following problems with Laplace T•ans:farm. Do not forget to invert the solution in Laplace domain back to time domain. DO NOT use software. Use only 6 basic Laplace pairs derived in class and Laplace Transform properties. Problem 3 + ± 1 3x(i) = 4g(t)+ 26g(/), x(0) = 1, ±(0) = 1 where g(t) is a unit step function u(t). Use transform of a derivative property when deriving. Laplace transform of the right-hand side of the given equation (consider that tt(0)-= 0 ) 
Problem 4 2(t)= (t), x(0) = 0 where f(t) is a piecewise-continuous function defined as follows: 
f(t) 
f(t)