the engine in the rocket is supposed to provide a constant thrust of 5000 KN. the turbopump unit in the engine nominally operates at 7000 rpm, and a result of design issue, the actual thrust provided by the engine oscillates harmonically with an amplitude of 10 KN at the same rotational frequency as the turbopump unit. the mass of the engine is m= 5000 kg. the rest of the rocket is much heavier than the engine and can be treated as being fixed. the engine is mounted to the rocket via two structural members, each of which can be modeled as consisting of a linear spring of stiffness k in a parallel with a dashpot with linear viscous damping coefficient c. determine the smallest values of c and k such that the static deflection due to the constant component of the thrust is less than 0.01 m and so that the vibration amplitude in the nominal operating regime is less than 0.001 m. ignore the stiffness and damping due to the piping. HINT: if x is measured from the equilibrium position of the engine that results from the combined effect of the thrust and gravity, then the engine is subject to an extremely applied forcing equal (10sinw0t) kn, where w0 is the rotational frequency of the turbo pump