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In the system shown in the given figure, r (t) = sin ωt. The steady-state response c(t) will exhibit a resonance peak at a frequency of—
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- 4 rad/sec
- 2√ 2 rad/sec
- 2 rad/sec
- √ 2 rad/sec
- 4 rad/sec
Correct Option: B
From given figure
| = | ||
| R(s) | s2 + 4s + 16 |
C.E. = s2 + 4s + 16.
on comparing this equation with the standard equation
s2 + 2 ξ ωns + ωn2 = 0
2 ξ ωn = 4 …(i)
ωn2 = 16 …(ii)
resonance peak frequency is given by
ωr = ωn √1 - 2ξ 2
from equations (i) and (ii)
ξ = 0.5
ωn = 4
Thus, ωr = 4√1 – 2(0·5)2
= 2√2.
