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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

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 Correct Answer 6040

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/m2 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 106/240 = 6040 rpm.

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