Question

An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

(a) 6040

(b) 3020

(c) 1424

(d) 955

I have been asked this question during an internship interview.

This is a very interesting question from Bifilar and Trifilar Suspension in section Simple Harmonic Motion of Machine Kinematics

Answer 1

Right choice is (a) 6040

To explain I would say: Given k1 = k2 = 16MN/m, k3 = k4 = 32MN/m, m = 240 kg

Here, k1 & k2 are the front two springs or k3 and k4 are the rear two springs.

These 4 springs are parallel, So equivalent stiffness

keq = k1 + k2 + k3 + k4 = 16 + 16 + 32 + 32 = 96MN/m^2

We know at resonance

ω = ωn = √k/m

2πN/60 = √keq/m               N =Engine speed in rpm

N = 60/2π√keq/m

  = 60/2π√96 x 10^6/240

  = 6040 rpm.