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Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation.
Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the system below, V, (1) İs the excitation and v.) is the response. (a) Find the system function: H(s). (b) If V, (t) = sin(2t)u(t), what is its Laplace Transform: K(s)? (c) Assuming zero initial conditions, with the input given in (b), what is the Laplace Transform of the output v,(t):V.(s)? (d) What is v,0)? (Hint: use partial fraction and inverse Laplace transform)
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