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2. Find the Magnitude and Phase values of f(t) = 5 eu(t) for w = -4,-2,0, 2, 4? a) Magnitude = { 2.24, 1.21, 5, 1.21, 2.24) Phase = (-75.97,-63.4, 0,63.4, 75.97} b) Magnitude = { 1.21, 2.24, 5, 2.24, 1.21) Phase = (-75.97,-63.4, 0, 63.4, 75.97} c) Magnitude = {2.24, 1.21, 5, 1.21, 2.24) Phase = {75.97, 63.4, 0, 63.4, 75.97 } d) Magnitude = { 1.21, 2.24, 5, 2.24, 1.21) Phase = {75.97, 63.4, 0, -63.4, -75.97 } e) Magnitude = { 2.24, 1.21, 5, 1.21, 2.24) Phase = {75.97, 63.4, 0, -63.4, -75.97 } f) Magnitude = (1.21, 2.24, 5, 2.24, 1.21) Phase = (-75.97,-63.4, 0, -63.4, -75.97)

Answer :

Final answer:

The Magnitude and Phase values of f(t) = 5 eu(t) for w = -4,-2,0, 2, 4 are:

Magnitude = { 5, 5, 5, 5, 5 }

Phase = { -4t, -2t, 0, 2t, 4t }

Explanation:

To find the Magnitude and Phase values of the function f(t) = 5 eu(t) for w = -4,-2,0, 2, 4, we can use Euler's formula and the formulas for Magnitude and Phase.

Euler's formula states that e^(ix) = cos(x) + i*sin(x), where e is the base of the natural logarithm, i is the imaginary unit, and x is a real number.

Let's evaluate the function for each value of w:

  1. For w = -4:
  2. f(t) = 5e^(-4t) = 5(cos(-4t) + i*sin(-4t))
  3. Magnitude = |f(t)| = |5e^(-4t)| = 5
  4. Phase = arg(f(t)) = arg(5e^(-4t)) = -4t
  5. For w = -2:
  6. f(t) = 5e^(-2t) = 5(cos(-2t) + i*sin(-2t))
  7. Magnitude = |f(t)| = |5e^(-2t)| = 5
  8. Phase = arg(f(t)) = arg(5e^(-2t)) = -2t
  9. For w = 0:
  10. f(t) = 5e^(0t) = 5(cos(0t) + i*sin(0t))
  11. Magnitude = |f(t)| = |5e^(0t)| = 5
  12. Phase = arg(f(t)) = arg(5e^(0t)) = 0
  13. For w = 2:
  14. f(t) = 5e^(2t) = 5(cos(2t) + i*sin(2t))
  15. Magnitude = |f(t)| = |5e^(2t)| = 5
  16. Phase = arg(f(t)) = arg(5e^(2t)) = 2t
  17. For w = 4:
  18. f(t) = 5e^(4t) = 5(cos(4t) + i*sin(4t))
  19. Magnitude = |f(t)| = |5e^(4t)| = 5
  20. Phase = arg(f(t)) = arg(5e^(4t)) = 4t

Learn more about finding the magnitude and phase values of a given function here:

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