A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge $\text{B}$. The mass moment of inertia of the rocker about $\text{B}$ is $10^{-4} \text{kg.m}^{2}$. The rocker arm dimensions are $\text{a=3.5 cm}$ cm and $\text{b=2.5 cm}$. A pushrod pushes the rocker at location $\text{A}$, when moved vertically by a cam that rotates at $\text{N rpm}$. The pushrod is assumed massless and has a stiffness of $\text{15 N/mm}$. At the other end $\text{C}$, the rocker pushes a valve against a spring of stiffness $\text{10 N/mm}$. The valve is assumed massless and rigid.
Resonance in the rocker system occurs when the cam shaft runs at a speed of ____________ $\text{rpm} (\textit{round off to the nearest integer}$).
- $496$
- $4739$
- $790$
- $2369$