(a) Find the Laplace Transform of the following function (i) f(t) = 5 - 3t + ? cos t (ii) f(t) = (3 + e^{6t})^2 (b) Ground vibration wave signal from an accelerometer recorded a reading in Laplace Function as shown in the following equation. Compute the inverse Laplace Transform of the function to obtain the real function of time, t, of the wave equation. Y(s) = 2 / (3 - 5s) (c) Solve the following Laplace Transform by using the respective methods (i) L{t^2 cos at} :- differentiation of transform (ii) L{e^{2t} t^3} :- First shift property
Added by Lu-S H.
Close
Step 1
### Part (a) - Find the Laplace Transform of the given functions #### For the function f(t) = 5 - 3t + t cos(t) ** Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 54 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the Laplace Transform of: e^{-t} sin 2t u(t - π). [Hint: sin 2t = sin 2(t - π)] A signal is given by: x(t) = { 2, 0 ≤ t < 1; t, 1 ≤ t < 2; e^{2t}, t ≥ 2 } i. Rewrite x(t) in terms of unit step function ii. Find the Laplace transform of x(t). Determine the inverse Laplace transform of the following functions i. Y(s) = (2 - 3s^2 + s^3) / s ii. Y(s) = (s - 6) / (s^2 + 2s + 4) By using the convolution theorem, find the inverse Laplace transform of: 2 / (s^2 + 4)^2
Madhur L.
Find the Laplace transform of each of the following functions: (a) f(t) = 5 + e^(-3t) + te^(-4t) (b) f(t) = sin(4t) + (t - 3)e^{-(t-3)} + 5/t (c) f(t) = t cos(4t) + t/5 (d) f(t) = (t - 1) cos[4(t - 1)] + t^2
Sri K.
3. Find the Laplace transform of the following functions a. f(t) = 3 cos(6t) b. f(t) = 1(t) + 2t cos(2t) c. f(t) = t sin(t) d. f(t) = sin(t) sin(3t) 4. Find the time functions of the following Laplace transforms. a. F(s) = 10 / (s(s+1)(s+10)) b. F(s) = (3s+2) / (s^2+4s+20) c. F(s) = 2(s+2) / ((s+1)(s^2+4)) d. F(s) = (2s^2+s+1) / (s^3-1)
Harsha M.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD