Question

A refrigerator unit having a mass of 35 kg is to be supported on three springs, each. having spring stiffness s. The unit operates at 480 rpm. If only 10% of the shaking force is allowed to transmit to the supporting structure, the value of stiffness will be nearly 

(a) 2.7 N/mm 

(b) 3.2 N/mm 

(c) 3.7 N/mm 

(d) 4.2 N/mm

Answer 1

Correct option is (a) 2.7 N/mm 

m = 35 kg

Total stiffness, s_equi = 3_s

N = 480 rpm

ω =  \(\cfrac{2\pi\times480}{60}\) 

= 50.2654 rad/s

ω_n = \(\sqrt{\cfrac{s_{equi }}m}\) = \(\sqrt{\cfrac{3s}{35}}\) = rad/s

Here ξ = 0 (No damping)

F_T = (10% of F_o)

= (0.1)F_o 

_{\(\cfrac{F_r}{F_0}\) =} 0.1 = ∈ ⇒ Transmissibility

\(\left(\cfrac{ω}{ω_n}\right)^2\) = 1 - 10 = - 9

(Not possible)

Taking (–ve)sign