The uniform 8–ft board is pushed down into the water so it makes an angle of θ = 30o with the water surface. If the cross section of the board 3 in by 9 in, and its specific weight is γ = 30 lb/ft3 , determine the length a that will be submerged and the vertical force F needed to hold this end in this position.

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