See307 systems and signals assignment - use direct

Question

SYSTEMS AND SIGNALS ASSIGNMENT -

Question 3: Use direct integration find the Laplace transform and the ROC of the following functions:

a) u(t)- u(t -1)

b) te^-tu(t)

c) t cos(ω₀t)u(t)

d) (e^2t - 2e^-t)u(t)

Question 4: Find the inverse Laplace transform of:

a) (2s + 5)/(s² + 5s + 6)

b) (3s + 5)/(s² + 4s +13)

c) (s +1)²/(s² - s - 6)

d) (2s +1)/(s +1)(s² + 2s + 2)

Question 5: For the system described by the following differential equations, find the system transfer function:

a) d²y/dt² +11 dy/dt + 24y = 5 dx/dt + 3x

b) d³y/dt³ + 6 d²y/dt² -11 dy/dt + 6y = 3 d²x/dt² + 7 dx/dt + 5x

c) d⁴y/dt⁴ + 4 dy/dt = 3 dx/dt + 2x

d) d²y/dt² - y = dx/dt - x

Note - Need questions 3, 4 and 5. Solved step by step and its systems and signals. Question 5 is to be solved with Laplace transform as well.