(Solved): A sketch of a valve and rocker arm system for an internal combustion engine is give in Figure P1.65 ...

A sketch of a valve and rocker arm system for an internal combustion engine is give in Figure P1.65. Model the system as a pendulum attached to a spring and a mass and assume the oil provides viscous damping in the range of $$?=0.01$$. Determine the equations of motion and calculate an expression for the natural frequency and the damped natural frequency. Here $$J$$ is the rotational inertia of the rocker arm about its pivot point, $$k$$ is the stiffness of the valve spring and $$m$$ is the mass of the valve and stem. Ignore the mass of the spring.