Question

Mi(t)+mᵤ (t)+Ku(t)=F₀ eʲʷᵗ

where F₀ is a real positive number and j² =−1. (30%) Assume u(t)=Ueʲʷᵗ where U is the complex magnitude of u(t). Find ∣U∣.

Answer 1

The magnitude of U is zero.

Step-by-step explanation:

To find the magnitude of U, we can substitute the given expression for u(t) in the equation and solve for U.

Substituting u(t)=Ueʲʷᵗ into the equation mi(t)+mᵤ(t)+Ku(t)=F₀eʲʷᵗ, we get:

mi(t) + mᵤ(t) + KUeʲʷᵗ = F₀eʲʷᵗ

(mi(t) + mᵤ(t))/F₀ + Ku(t) = U

Comparing the real and imaginary parts of this equation, we get:

mi(t) + mᵤ(t) = 0 (since both sides must be equal to U)

Thus, the magnitude of U is zero.