QUESTION 11 Find the solution of x' + 2x' +x=f(t), x(0)=1, x'(o=0, where f(t) = 1 if t< 2; and f(t) = 0 if t> 2.
Find the Laplace Transform of f(t)=0 if t< 1; f(t) = t if 1sts 2; f(t)=0 if t> 2.
Need solution pls... 1. Find the Fourier transform of 0 <t<2 (a) f(t) = 1+ -2<t<0 otherwise a > 0 (b) f(t) = Se-at eat t> 0 t < 0 () f(1) = { cost t> 0 t < 0 0 Answer: 1 - cos 20 (a) (b) 2a al + m2 (c) 1 + jo (1+0)2 + 1
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
QUESTION 10 Find the Laplace Transform of f(t) = 0 ift<1: f(t) = tiflsts 2: f(t) = 0 ift> 2. ign 5
Find the length of spiral curve T() = ----- 0 < > < 2”
QUESTION 1 5 Find the Laplace transform of the function f(t) t, 0<t<1 1, t > 1
Find the solution of the given initial value problem: y" + y = f(t); y(0) = 6, y'(0) = 3 where f(t) = 1, 0<t<3 0, įst<<
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Find the Laplace transform of the function f(t) = t, 0 <t<1 1, t>1 s e ОА 52 e-(s-1) OB S $2 1- e-s ос. $2 S OD S 1-e OE S