GATE ME 2022 Set 2 — Question 40
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Theory of Machines & Vibrations → Forced Vibration → Harmonic Excitation Response
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Question
A spring mass damper system (mass , stiffness , and damping coefficient ) excited by a force , where , and are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as (i) to (iv)) are shown just to the right of the system figure. In the figures of the responses, is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and those are not drawn to any specific scale.
Four different parameter and forcing conditions are mentioned below.
(P) and
(Q) and
(R) and
(S) and Which one of the following options gives correct match (indicated by arrow ) of the parameter and forcing conditions to the responses?
(P) and
(Q) and
(R) and
(S) and Which one of the following options gives correct match (indicated by arrow ) of the parameter and forcing conditions to the responses?
Correct answer
(C) (P) arrow (i), (Q) arrow (iv), (R) arrow (ii), (S) arrow (iii)
Solution
The qualitative responses can be matched as follows:
1.(P) and : This is the case of damped resonance. The steady-state response has a constant finite amplitude. This matches plot (i).
2.(Q) and : Negative damping leads to an unstable system where the amplitude grows exponentially over time. This matches plot (iv).
3.(R) and : This is undamped resonance. The amplitude of the response grows linearly with time. This matches plot (ii).
4.(S) and : This represents the phenomenon of beats, where the amplitude modulates periodically due to the proximity of the forcing frequency to the natural frequency. This matches plot (iii).
Thus, the correct match is (P) (i), (Q) (iv), (R) (ii), (S) (iii).Continue learning with Success Tracker
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