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LAPLACE TRANSFORMS & FUNCTIONS EXAM
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LAPLACE TRANSFORMS & FUNCTIONS EXAM
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LAPLACETRANSFORMS &
FUNCTIONS
EXAM
Unit impulse δ(t) - answer ✅✅1
A function that is 0 for all time, except at time 0, it has an infinite magnitude.
Area underneath the curve = 1
Approximates signals for behaviors such as a hammer strike.
Unit Step u(t) - answer ✅✅1/s
A function that is 0 for all time up to t, except at time 0, it steps put to a value of 1.
1 - answer ✅✅1/s
Area underneath the curve = 1
Unit Ramp At - answer ✅✅A/s²
, A straight line with a slope of 1 and y intercept of 0
Area underneath the curve =1/s²
tⁿ⁻¹ ÷ (n - 1)! - answer ✅✅1/sⁿ
tⁿ - answer ✅✅n!/sⁿ⁺¹
A parabola or cubic function
e^(-at) - answer ✅✅1/(s+a)
t * e^(-at) - answer ✅✅1/(s+a)²
tⁿ⁻¹ ÷ (n - 1)! * e^(-at) - answer ✅✅1/(s+a)ⁿ
tⁿ * e^(-at) - answer ✅✅n!/(s+a)ⁿ⁺¹
sin (bt) - answer ✅✅b/(s²+b²)
cos (bt) - answer ✅✅s/(s²+b²)
sinh (bt) - answer ✅✅b/(s²-b²)
cosh (bt) - answer ✅✅s/(s²-b²)
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