(a) xi (t) =4(sin(31) + cos(3t)] (b) x2(t) = sin(41) 1.18 For each of the following...
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
(3e-4 -8t +9 Consider the vector-valued functions xi(t) = | (-2+2 + 3t) and 22(t) = 3e-4t a. Compute the Wronskian of these two vectors. Wx(t) = (67 – 33t+27)e-4t), b. On which intervals are the vectors linearly independent? If there is more than one interval, enter a comma-separated list of intervals. The vectors are linearly independent on the interval(s): (-infinity,1),(1,4.5),(4.5, infinity), help (intervals). c. Find a matrix P(t) = (Pu(t) P12(t)) so that 21 and 22 are fundamental solutions...
2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t)) 2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t)) c)E(t)=(tcos(t), t sin(t))
help with 3.2-2 3.2-1 Sketch the following functions: (a)TI (3t/4); (b) A(7x/10); (c) П (t-1/4) ; (d) sinc [(nf-2t)/5]; (e) sinc (2tt/5); ( f) sinc (π ) Π (96) 3.2-2 Use direct integration to find the Fourier Transform for the signal in Problem 3.2-1(a)(b)(c)
3.5 Determine the Laplace transform of each of the following functions by applying the properties given in Tables 3-1 and 3-2. (a) xi(t) = 16e-2t cos 4t u(t) (b) x2(t) = 20te-21 sin 4t u(t) (c) x3(t) = 10e-34 u(t – 4) Table 3-1: Properties of the Laplace transform for causal functions; i.e., x(t) = 0 for t < 0. Property x(t) 1. Multiplication by constant K x(t) 2. Linearity K1 xi(t) + K2 x2(t) X($) = L[x(t)] K X(s)...
1. Determine the Laplace transform of the following signals e* .11(t) ; (b) g(t)=Icos(2) + sin(2t)j.u(1-3) ; (c) h(t)-t-e-21. cos(30.11(1) 2. Determine the Laplace transform of the non-periodic signal shown below: h(t) 0 1 2 3 4 t 3. Determine the Laplace transform of the periodic waveforms shown below: fa) f(t) 0 2T 4T 6T 8T 4. Determine the inverse Laplace transform of the following signals 2s (b) G)6s+12 H(s) =s.(14%) (a) F(s)-De (c) (2s +1)(s1 +5s +6 5. Using...
Consider the following three signals: a) X(t)= e 104 b) x2(t)=sin(2net)+sin(20ạt) (i.e. a combination of 1Hz and 10 Hz frequencies); c) xz(t)=e'sin(at)u(t). Calculate analytically (or derive from the tables of standard transforms) their Fourier transforms and unilateral Laplace transforms. Compare the Fourier and Laplace transforms and comment on relations between the Fourier transform and the unilateral Laplace transform. Page 1 ECCE 302 Signals and Systems Laboratory Transforms d) Fourier transform YY(6) of some unknown signal xx(6) is given as follows:...
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5. Let x(t) be a signal with x(t) = 0 for t <3. For each signal given below, determine the values of t for which it is guaranteed to be zero....