Question

potion in Jitude. The Scillating due Why? Problems Instructions: You must complete the first 3 problems and one of the Inst two problems of your choice). Problem 1: The instrument shown on mu of 43 kw and is spring-mounted to the horizontal base. If the amplitude of vertical vibration of the base is 0.10 mm, calculate the range of frequencies of the base vibration which mal be prohibited if the amplitude of vertical vibration of the instrument is not to exceed 0.15 mm. Each of the four identical springs has a stiffness of 7.2 kN/m.

Answer 1

Given that,

Mass, m = 43 kg

Stiffness, k _e = 7.2 k N/m

Answert » Mass of the machine, m-313kg. Veoutraal viberation of the base, S = o.lomm Shiffress of spring, K - 7.2kNim so far four spring, Overall stiffnessk=28.5 kNim -) Amplitude of vibration of the instrument is not to exceed = 0,15mm. ( FO = ks ] .: Wwth

28,8X103 V m3 Win = 25 879 radis "5:25 | colt (25:879) 2o. 666 1-6 5 7a) 5-0.666 By solving, we get ws 14.90 Com) . wz 33.409 (t = w therehore, range of Et S. 2: 377) frequency, fo ) +2.5.317