The acceleration of a particle is given by a =-ks^2, where a is in meters per second squared, k is a constant, and s is in meters. determine the velocity of the particle as a function of its position s. evaluate your expression for s=7 m if k=0.3 m^-1s^-2 and the initial conditions at time t = 0 are so = 4 m and vo = 14 m/s.

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