A closed-loop system is shown below. When will the system

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A closed-loop system is shown below. When will the system is very much underdamped?

1. T₁ << T₂
2. T₁ = T₂
3. T₁ > T₂
4. T₁ >> T₂

Correct Option: A

From figure C.E. ⇒ 1 + G(s) H(s) = 0

1 +	1	. 1 = 0
	sT₁(1 + sT₂)

or
sT₁ + sT₁T₂ + 1 = 0

s₂ +	s	+	1	= 0......…(i)
	T₂		T₁T₂

on comparing equation (i) with the standard equation
s² + 2ξω_ns + ω_n² = 0,
we get
2ξω_n = 1/T₂
ω_n² = 1/T₁T₂
or
ω_n = 1/√T₁T₂
For system to be strong underdamped
ξ << 1
or
√T₁T₂/2T₂
<< 1 or T1 << T2 (with ξ < 0·5)
Hence alternative (A) is the most correct choice.