3. Write the following in positive cosine form: a) 6*cos(2t 1E6*t-18°) b) 3*sin(2t 1E3 t+184°) c)...
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
Problem 6. (10 pts) Write down the following in the form of x(t) = A cos(2t + o), where A> 0 x(t) = sin(2t + 7) + cos2t
Question 5. (8 points) Find the following: (a) L{t- sin(2t)} (b) C{2* * cos(t)} (c) c- )4+{2+2 +5} 4s S2 + 2s + 5 (d) C-1 6e-3 $2 +1
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
Question 5 Write the complex number in rectangular form. -3(cos 225° +i sin 225°) Question 6 Write the complex number in polar form. Express the argument in degrees. 3cos Oº+isin 0°) 3[cos 180°+ i sin 1809) 3[cos 90° + i sin 90°) O 3(cos 270° Fisin 270°F
QUESTION 6 Find 2 45 s2 + 25-3 5 (write 5/6 by and sin(2t) or cos(31) by sin(2t) or cos(3t). 6.ey-3t) by e-3t 5 points
2. Write the cosine based phasors in complex number form (a + b) for the following time functions. a. 10 cos(ot + 90) b. 10 sin(ot +90) c. 10 sin( 30) 3. Determine the time-domain functions associated with each of the following phasors. a. -2-i2 c. 4-i6 Write the mesh equations in matrix form (you do not have to solve them) for the following eircuit, using the phasor approach. (Hint: It helps to write the phasor quantities on the circuit...
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2 2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
all parts -2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...