GATE ME 2021 Set 1 — Question 42

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MCQ+2 / -0.67HardSDOF Free VibrationFree VibrationTheory of Machines & VibrationsResonanceForced Vibration

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 104 kg.m210^{-4}\text{ kg.m}^2. The rocker arm dimensions are a=3.5 cma = 3.5\text{ cm} and b=2.5 cmb = 2.5\text{ cm}. A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at N rpmN\text{ rpm}. The pushrod is assumed massless and has a stiffness of 15 N/mm15\text{ N/mm}. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm10\text{ N/mm}. The valve is assumed massless and rigid.
Tappet valve mechanism diagram showing rocker arm ABC hinged at B with pushrod at A and valve spring at C
Resonance in the rocker system occurs when the cam shaft runs at a speed of ________ rpm (round off to the nearest integer).
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