Obtain the laplace transform of the given function

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Reference no: EM13983033

Systems Modeling Laboratory

Problem 1- Solve the following differential equations:

(i) dy/dt + 2y =12              y(0) = 10

(ii) d2y/dt2 + 3(dy/dt) + 2y = 24                   y(0) = 10  y'(0) = 0           

(iii) d2y/dt2 + 2(dy/dt) + 5y = 20                 y(0) 0       y'(0) = 10                          

Problem 2- Solve the following differential equations where the input is f(t) = 5t and the initial conditions are zero. Plot the response of the following models for 0 ≤ t ≤ 1.5

(i)  3x·· + 21x· + 30x = f(t)                      

(ii) 5x·· + 20x· + 65x = f(t)                      

(iii) 4x·· + 32x· + 30x = 3f·(t) + 2f(t)                      

Problem 3 - Obtain the Laplace transform of the following function:

x(t) = t

x(t) = (2 - ae-2t + be-3t )

x(t) = 10cos(2t)

Problem 4 - Calculate the Laplace transform of the following function:

v(t) = 3e-2t sin 5t + 4e-2t cos5t

Problem 5 - Calculate the inverse transform of the following functions:

(i) F(s) = 100(s + 3)/(s+1)(s+2)(s2+2s+5)

(i) Y(s) = (10/(s + 2)) + (48/(s+2)(s2+16))

(iii) Expand the following transform using Partial-Fraction expansion. Also calculate the inverse transform.

X(s) = 4s + 3/s(s2 + 6s + 34)

Problem 6- Obtain the inverse Laplace transform x(t) for each of the following transforms:

(i) X(s) = 7s+2/s2+6s+34

(ii) X(s) = 4s+3/s(s2+6s+34)

Problem 7 - Solve the following problems:

(i) x·· + 7x· + 10x = 20    x(0) = 5     x·(0) = 3

(ii) 5x·· + 20x· + 20x = 28    x(0) = 5     x·(0) = 8

Reference no: EM13983033

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