There was a mistake made when a special machine was ordered

There was a mistake made when a special machine was ordered from Europe. The purchase order should have specified on 120 v 60 hz electricity available here in the United States. Because there was no such specification, the manufacturer shipped the standard model which operates on the 220 v 50 hz available in Europe. It is unfeasible to return the machine. The problem was brought to the electrical engineering department of your company which applied a transformer to increase the line voltage to 220 v. In that the motor in the machine was designed to operate at 1414 rpm on the frequency available in Europe, it will run faster in proportion to the ratio of the American and European frequencies. What is the operating speed on the American frequency in rpm? Unfortunately the machine resonates when operated on 60 hz electricity. What is the resonant frequency of the machine in radians per second? The problem has been referred to the mechanical-engineering department of your company, and your supervisor has assigned you the task of quelling the undesired vibration by applying a vibration absorber. A block of steel weighing 5 lbs. has been found which can be used as the mass element of the vibration absorber. What is the mass of this block in units such as inches, pounds, and seconds? What stiffness spring is needed for this vibration absorber in units such as inches and pounds?

Solution

Changing the power supply frequency means the motor will spin proportionately faster by 60/50 or 120%

then if 1414 rpm was the nominal european speed, in US it spins at 1.2*1414= 1696.8 rpm

Resonate effect:Due to the difference in frequency a resonance will occur at a common multiple of 50 and 60 , say 300 Hz. There are beat effects due to the difference of (60-50) hz. 1Hz = 6.283 R/s

c) vibration absorber: mass of 5lb (poundal) = 5*32.2 lb wt = 161ft lb /sec²

d) sqrt (K/M) = frequency in r/s where K is the spring stiffness ( lb /s² ), m=lb