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20 questions
Laplace Transform transforms a function from
f(t) to F(s)
F(s) to f(t)
f(t) to f′(t)
f"(t) to f′(t)
Which one is the correct definition of Laplace Transform?
F(s)=∫0∞e−stf(t)dt
F(s)=∫0tf(t)g(t−u)
What is the Laplace Transform for f(t)=t3 ?
s31
s32
s46
s33
What is Laplace Transform for e−2t ?
s−21
s+21
s2
s21
What is Laplace Transform for sin 2t ?
s2+22
s2+2s
s2+42
s2+4s
What is Laplace Transform for 6 sin 2t ?
s2+42
s2+4s
s2+46
s2+412
Define this property: L(f(t)eat)=F(s−a)
Linearity Property
First Shifting Property
Convolution Theorem
Second Shifting Property
L(e3tt) Based on first shifting property, what is a value?
1
2
3
4
Find L(e3tt)
(s2)1
(s−3)21
(s−2)21
(s)1
L(e2t sin t) What is a and f(t)?
a=2, f(t)=e2t
a=4, f(t)=cos t
a=2, f(t)=sin t
Find L(cos t)
s2+11
s2+41
s2+1s
Find L(e2tsin 2t)
(s−1)2+11
(s−2)2+4s
(s−4)2+1s
Find L(t3−3t2+5t)
s46−(s36)+s25
s33−(s(2)1)+s1
s32−(s(2)3)+s5
Find L(e3t(t3−3t2+5t))
(s−3)42−⎝⎛((s−3)3)3⎠⎞+(s−3)25
(s−3)46−((s−3)36)+(s−3)25
(s−3)32−((s−3)(2)3)+s−35
L(t cos 6t) Which Laplace property is use to solve this?
Linearity Property
Derivative of Laplace Transform
First Shifting Property
Second Shifting Property
L(t sin 4t) What is n, f(t) and F(s)?
n=1, f(t)=sin 4t, F(s)=s2+16s
n=4, f(t)=t, F(s)=s2+164
n=1, f(t)=cos 6t, F(s)=s2+14s
Find L(tsin 4t)
s2+42
−(s2+4)24s
−(s2+16)28s
L(sin2t) What is f(t), f′(t) and f(0) ?
f(t)=sin2t, f′(t)=2 cost, f(0)=0
f(t)=sin2t, f′(t)=sin 2t, f(0)=0
f(t)=cos2t, f′(t)=− sin2t, f(0)=1
What is the formula for Laplace First Order Derivative?
L(f′(t))=sF(s)−f(0)
L(f"(t))=s2F(s)−sf(0)−f′(0)
L(f′(t))=s2F(s)−f(0)
What is the formula for Laplace Second Order Derivative?
L(f′(t))=sF(s)−f(0)
L(f"(t))=s2F(s)−sf(0)−f′(0)
L(f"(t))=s2F(s)−f(0)
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