Q2. Piston of an internal combustion engine can be represented as a non-offset slider crank mechanism as shown in the figure to the right. Spring represents the gas inside the chamber excluding the combustion and it is at the free length when 012 = 0; viscous damper represents the energy dissipation due to engine oil. If the links 2 and 3 can be assumed massless and neglecting joint frictions: a) Perform the position, velocity, and acceleration (PVA) analysis of the mechanism for the given closure in terms of input variable 012 and a constant angular velocity 012 (express variables 013, S14, $14, and S14 in terms of 012, 012) b) Using the virtual work method, find the expression for the combustion force F (You don't need to expand the results of PVA analysis as long as you express them symbolically at an earlier step). a2 A A 12/ $14 B g=9.81 m/s 013 M F C c) For the given numerical values plot the force vs time graph needed to maintain a constant angular velocity 12 of 4000 rpm at steady state. kN a = 5 mm, a3 = 15 mm, M = 0.5 kg, k = 50-, m Ns c=100- m