Answered the question below.
If you have any doubt ask in the comment section.
Please give rating.
No.8 Express the following in terms of sinusoidal functions: 1. 10e/45 + 10e-145-8e-160 - 8e360 12e...
(e) Express Laplace transforms of the following functions in terms of F(8)- (f(t)) 0 0
(e) Express Laplace transforms of the following functions in terms of F(8)- (f(t)) 0 0
Express the following functions in terms of unit step functions and find the Laplace transforms. 2 f(t)= 0 0<ts 1<t<21 t> 21 sint (12 marks)
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
6. Express solutions of the following in terms of the special functions defined in lectures [do not derive these solutions): (a) (1-x2)y"-2xy' + n (n + 1 )y = 0. conditions g(-1)-(1)", (1)1 -1-x < 1, write down the solution that satisfies the boundary )sine de sin de+n(n+1)7-0,0T, write down the general solution and then the solution and 27-periodic with respect to θ. that is bounded for YAc
6. Express solutions of the following in terms of the special functions...
a) Q=1 aP+ b Transpose the formula to express P in terms of Q. (3 marks) b) Determine the equilibrium level of income given: C = 0.6Y + 120 1 = 45 G = 634 X = 160 M = 0.45Y + 8 all in £m. (7 marks)
16 , Eo Problem 1 (8 pts): An experimentalist is examining a kind of non-interacting identical particles that could be either spinless bosons or spin-half fermions by putting a number of them inside a potential and measuring the energy levels of the system, but without being able to resolve the degeneracy of each level. Energy levels do not depend on the particles' spin. The following values of the energy are observed: No particles: 0 -5€ 1 particle: E, 2E, 5E...
6. Express solutions of the following in terms of the special functions defined in lectures [do not derive these solutions]: (a) (1-2)y" - 2ry n(n+ 1)y 0, -1S1, write down the solution that satisfies the boundary conditions y(-1) = (-1)", y(1) = 1; to sin θ + n (n + 1)7-0 0 θ π, write down the general solution and then the solution sin 0 dø Sin 0 that is bounded forve e [0, π] and 2r-periodic with respect to...
9–27. For each of the following functions f(t), (a) express f(t) in terms of on-off switches X[a,b)(t), (b) express f(t) in terms of translates h(t – c) of the Heaviside function h(t), and (c) compute the Laplace transform F(s) = £{f(t)}. so if 0 <t<2 It-2 if 2 <t<oo So if 0 <t<2 It if 2 <t< oo 11. 40) - ſo if 0 <t< 2 It +2 if 2 <t<oo 12. f(t) = {o |(t – 4)2 if0 <1<4...
a only
5.3.5 Exercises Ex. 5.11. Express the following functions in terms of Heaviside step func- tions and find their Laplace transforms: 0t 2 0t3 t, (a) f(t) (b) f(t) t4 2< t < 4 3 t 3<t < 6 3, 4 t 0, 6 t
okmarks Complete the following questions and submit them to 1. Sketches the following sinusoidal functions: o y=2 sin (x + 180°) o y = 42 cos 3(x - 180°) + 2 o y=-2 cos (44X + 90°) 2. Create one equation for cos(e) and one equation for sin(O) fo 100 200 300