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Use Laplace transform to solve the initial value problem x" – 9x = e¯3t , x(0) = 1, x'(0) = –1 1, x'(0) = -1 %3D (7 if 3 < t

Use Laplace transform to solve the initial value problem x" – 9x = e¯3t , x(0) = 1, x'(0) = –1 1, x'(0) = -1 %3D (7 if 3 < t

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter6: Ratio, Proportion, And Probability
Section6.8: The Multiplication Principle
Problem 1E
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5. t Ticketmaster | Chec... B. Double Tree by Hilt... uites St... 1/ 1 + %68 3s+1 12. 42 s3+4s2-21s s(s2+4) 2s+5 [7-e4sT s2+6s+34. 3-S -8 ,if 3 <t < 4 ,otherwise 2. Let f(t) = %3D a) Give a formula for f(t) using the unit step function. b) Determine the Laplace transform of f(t) 3. Use Laplace transform to solve the initial value problem x" – 9x = e-3t ; x(0) = 1,x'(0) = –1 Ə = X6 7 ,if 3 <t < 4 Let f(t) =30 .otherwise 4. %3D a) Determine the Laplace transform of f(t) b) Use Laplace transform to solve the initial value problem x" + 9x = f (t); x(0) = 0, x'(0) = 0 %3D %3D In this exercise, your task is to find the Laplace transform F(s) = L[f(t)] f(t) = t · cos(4t). For that, compute the second derivative and write the e f"(t) =...-16f(t) (don't forget to use the product rule). Then apply the I transform on both sides and use properties from the handout to turn it into a equation with the unknown F(s). After that, solve it to get the answer. %3D [(1)]] %3D 6. A 4-kg mass is attached to the end of a spring with spring constant 16N/m. I first experiment, the body is pushed from the equilibrium position with initial v v(0) = 20m/s to the right, stretching the spring. In the second experiment, the pulled 7 m to the right, stretching the spring and after that it is released. Find position functions x(t) in each case and compare the amplitudes and periods Oscillation in
Transcribed Image Text:5. t Ticketmaster | Chec... B. Double Tree by Hilt... uites St... 1/ 1 + %68 3s+1 12. 42 s3+4s2-21s s(s2+4) 2s+5 [7-e4sT s2+6s+34. 3-S -8 ,if 3 <t < 4 ,otherwise 2. Let f(t) = %3D a) Give a formula for f(t) using the unit step function. b) Determine the Laplace transform of f(t) 3. Use Laplace transform to solve the initial value problem x" – 9x = e-3t ; x(0) = 1,x'(0) = –1 Ə = X6 7 ,if 3 <t < 4 Let f(t) =30 .otherwise 4. %3D a) Determine the Laplace transform of f(t) b) Use Laplace transform to solve the initial value problem x" + 9x = f (t); x(0) = 0, x'(0) = 0 %3D %3D In this exercise, your task is to find the Laplace transform F(s) = L[f(t)] f(t) = t · cos(4t). For that, compute the second derivative and write the e f"(t) =...-16f(t) (don't forget to use the product rule). Then apply the I transform on both sides and use properties from the handout to turn it into a equation with the unknown F(s). After that, solve it to get the answer. %3D [(1)]] %3D 6. A 4-kg mass is attached to the end of a spring with spring constant 16N/m. I first experiment, the body is pushed from the equilibrium position with initial v v(0) = 20m/s to the right, stretching the spring. In the second experiment, the pulled 7 m to the right, stretching the spring and after that it is released. Find position functions x(t) in each case and compare the amplitudes and periods Oscillation in
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