For a rectangular cross-section silicon beam simp support at its both ends with a length of 10 cm, width 3mm and thickness 1 mm, compute its first mode resonant frequency. Drive the scaling law for the resonant frequency of such beam, assuming an isometric length scaling. Using such a scaling law, compute the resonant frequency of the beam when you scale it down 1,000 times smaller.

Liquid flows at steady state at a rate of 2 lb/'s through a pump, which operates to raise the elevation of the liquid 100 ft from control volume inlet to exit. the liquid specific enthalpy at the inlet is 40.09 btu/lb and at the exit is 40.94 btub. the pump requires 3 btu/s of power to operate. if kinetic energy effects are negligible and gravitational acceleration is 32.174 tt/s, the heat transfer rate associated with this steady state process is most closely 1)-2,02 btu/s from the liquid to the surroundings 2)-3.98 btu/s from the surroundings to the liquid. 3)-4.96 btu/s from the surroundings to the liquid. 4)-1.04 btu/s from the liquid to the surroundings.