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Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: 0< t < 1 (sin(nt), 10, 1

Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: 0< t < 1 (sin(nt), 10, 1

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 26E
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Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: (sin(at), 0, 0<t<1 1 <t y" +4y= Y(s) = Now find the inverse transform to find y(t) = Hint: write the right hand side in terms of the Heaviside function. (Use step(t-c) for uc(t).) Note: 7 (s² + 7²) (s² + 4) 7T y(0) = 0, y'(0) = 0 π² 4 s² + 4 S² + π²
Transcribed Image Text:Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: (sin(at), 0, 0<t<1 1 <t y" +4y= Y(s) = Now find the inverse transform to find y(t) = Hint: write the right hand side in terms of the Heaviside function. (Use step(t-c) for uc(t).) Note: 7 (s² + 7²) (s² + 4) 7T y(0) = 0, y'(0) = 0 π² 4 s² + 4 S² + π²
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