Question

p_w from vi Given 1. The voltage and current are given by v(t) = V, cos (27fyt + O,) (Volts) and i(t) = I; cos (2Tf;t + 0;) (Amps) for t to seconds, respectively. Note that neither v(t) or i(t) are given for t <to, and that to / 0 seconds. 2. The initial value of w(t) at t = to is given in the parameter file as wo 3. The parameters Vu, Ii, fu, fi, Ou, 0i, to, and wo can be found in the Parameter file for this problem. Do: a) Find the power absorbed by element r, p(t), for t > to. Express the answer in the following form: p(t) = K\ cos (2t f^t+ 01) + K2 cos (2t f2t +02) (Watts) over t > to (seconds) where K K2, fi, f2, 01, and 02 are numerical values that you determine. Use the following trigonometric identity, cos(a) cos(3) = cos(a - B) + cos(a B)]. Note that both fi and f2 must be greater than zero, and that fi < f2. p(ta)dt b) Find w(t) = Be sure to double underline the final answers and include units for all parts. Hints: 1. Rememeber that p(t) = v(t)i(t) 2. Choose a and 3 so that fi and f2 are both greater than zero. Note that a f B. to 3. Use the relationship w(t) = p(t)dt, and the information given to find to -OX -0 w(t) in part b. Note that tr is a dummy variable of integration

 Vv = 8 V 
  Ii = 5 A 
  fv = 19 Hz 
  fi = 11 Hz 
  theta_v = 120 degrees 
  theta_i = 25 degrees 
  t_0 = -500 mseconds 
  w_0 = 6 Joules 

Answer 1

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