the form of the transforms found for the functions above, state what form (c) Find the roots of the denominator of y and therefore factorise it. Considering A mechanical system is governed by the following ODE with the initial conditions (a) Using the shift theorem, write down the transforms of the following two shown: dy + 145y = 0, y = 2, dt dy 16 -0 when t= 0. dt Solve the equation fully with the following steps. functions: g(t) = Be-at cos(wt), h(t) = Ceat sin(wt). (b) Use the properties of the Laplace transform to find the original signal y will have.
the form of the transforms found for the functions above, state what form (c) Find the roots of the denominator of y and therefore factorise it. Considering A mechanical system is governed by the following ODE with the initial conditions (a) Using the shift theorem, write down the transforms of the following two shown: dy + 145y = 0, y = 2, dt dy 16 -0 when t= 0. dt Solve the equation fully with the following steps. functions: g(t) = Be-at cos(wt), h(t) = Ceat sin(wt). (b) Use the properties of the Laplace transform to find the original signal y will have.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. A mechanical system is governed by the following ODE with the initial conditions
shown:
162y
+145y = 0, y = 2,-
+8 dy
dy
dt²
dt
=0 when t = 0.
dt
Solve the equation fully with the following steps.
(a) Using the shift theorem, write down the transforms of the following two
functions:
g(t)= Beat cos(wt), h(t) = Ce-a sin(wt).
(b) Use the properties of the Laplace transform to find y.
(c) Find the roots of the denominator of y and therefore factorise it. Considering
the form of the transforms found for the functions above, state what form
the original signal y will have.
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