You intend to gently place several steel needles on the free surface of the water in a large tank. The needles come in two lengths: Some are 5cm long, and some are 10cm long. Needles of each length are available with diameters of 1mm,2.5mm and 5mm. Make a prediction as to which needles, if any, will float. 1.37 An important equation in the theory of vibrations is mdt2d2x+cdtdx+kx=f(t) where m(kg) is the mass and x(m) is the position at time t(s). For a dimensionally consistent equation, what are the dimensions of c,k, and f ? What would be suitable units for c, k, and f in the SI and BG systems