Answer:
t ≤ 0.31s
Explanation:
Given
Frequency = 0.1Hz
Dynamic Error:
σ = 1 - M(σ)
From the question
σ= 1 - M(σ) ≤ 2%
1 - M(σ) ≤ 0.02
The above corresponds to
M(σ) = 1/(1 + (wt))² ≥ 100% - 0.02
M(σ) = 1/(1 + (wt))² ≥ 1 - 0.02
M(σ) = 1/(1 + (wt))² ≥ 0.98
Since frequency = 0.1Hz
w = 2πf =
w = 0.628571428571428
w = 0.628rads
So, M(0.628) = 1/(1 + (0.628t)²) ≥ 0.98
Solving 1/(1 + (0.628t)²) ≥ 0.98 we get that
t ≤ 0.31s
