Using Routh’s stability criterion, answer the following parts: (a) Find how many roots with positive real parts are there for Q(s) = s 3 + s 2 + 20s + 78 = 0. (b) Find the range of K such that Q(s) = s 3 + 3Ks2 + (K + 2)s + 4 has all roots in the left half plane. (Here, K is a design parameter.)

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed