Calculate a = x+y, b = z + 1, then keep numbers a and b. Questions marked with *** are to be graded. 1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following transforms: a(s+2) *** a) X(s)= s(s+b) 2(s+2) b) X(s)= s(s+a)(s+b) 2. Obtain the inverse Laplace transform for the following transforms. a) F(s)= as+b b) F(s)= 5s+2 (s+a)(s+b)² 3. Obtain the solution x(t) of the the following differential equations: a) x+ax=0, x(0)=b, x(0) = 0 b) 2x+2x+x=a, x(0)=0, x(0)=b 4. Obtain the inverse transform of the following. If the denominator of the transform has complex roots, express x(t) in terms of sin() and cos(). *** a) X(s)= b) X(s)= 4s+a +8s+b s³+as+6 s(s+b) 5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial conditions. a) ax+20x+bx = f(t) b) x+ax+bx=3f(t)+2f(t)
Calculate a = x+y, b = z + 1, then keep numbers a and b. Questions marked with *** are to be graded. 1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following transforms: a(s+2) *** a) X(s)= s(s+b) 2(s+2) b) X(s)= s(s+a)(s+b) 2. Obtain the inverse Laplace transform for the following transforms. a) F(s)= as+b b) F(s)= 5s+2 (s+a)(s+b)² 3. Obtain the solution x(t) of the the following differential equations: a) x+ax=0, x(0)=b, x(0) = 0 b) 2x+2x+x=a, x(0)=0, x(0)=b 4. Obtain the inverse transform of the following. If the denominator of the transform has complex roots, express x(t) in terms of sin() and cos(). *** a) X(s)= b) X(s)= 4s+a +8s+b s³+as+6 s(s+b) 5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial conditions. a) ax+20x+bx = f(t) b) x+ax+bx=3f(t)+2f(t)
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 12T: Expand 3(x2)5+4(x2)3 by using Pascal’s Triangle to determine the coefficients.
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Transcribed Image Text:Calculate a = x+y, b = z + 1, then keep numbers a and b.
Questions marked with *** are to be graded.
1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following
transforms:
a(s+2)
***
a) X(s)=
s(s+b)
2(s+2)
b) X(s)=
s(s+a)(s+b)
2. Obtain the inverse Laplace transform for the following transforms.
a) F(s)=
as+b
b) F(s)=
5s+2
(s+a)(s+b)²
3. Obtain the solution x(t) of the the following differential equations:
a) x+ax=0, x(0)=b, x(0) = 0
b) 2x+2x+x=a, x(0)=0, x(0)=b
4. Obtain the inverse transform of the following. If the denominator of the transform has
complex roots, express x(t) in terms of sin() and cos().
***
a) X(s)=
b) X(s)=
4s+a
+8s+b
s³+as+6
s(s+b)
5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial
conditions.
a) ax+20x+bx = f(t)
b) x+ax+bx=3f(t)+2f(t)
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