GATE ME 2021 Set 1 — Question 42
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Theory of Machines & Vibrations → Forced Vibration → Resonance
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Question
A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is . The rocker arm dimensions are and . A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at . The pushrod is assumed massless and has a stiffness of . At the other end C, the rocker pushes a valve against a spring of stiffness . The valve is assumed massless and rigid.
Resonance in the rocker system occurs when the cam shaft runs at a speed of ________ rpm (round off to the nearest integer).

Correct answer
(B) 4739
Solution
1.Calculate equivalent stiffness at point C: .
2.Calculate equivalent mass at point C: .
3.Natural frequency .
4.Frequency in Hz: .
5.Resonance speed in rpm: . Rounding to the nearest integer gives 4739 rpm.
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