A sketch of a valve and rocker arm system for an internal combustion engine is give in Figure. Model the system as a pendulum attached to a spring and a mass and assume the oil provides viscous damping in the range of 3= 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. Hint: apply Lagrange equation method Rocker arm 0 J k m Solution: Ꮎ Follower k Valve spring Oil Cam m Valve l x