Find out force transmitted to the foundation:

A machine contains weight 1200 kg is mounted on springs of net stiffness 2 × 106 N/m. The machine is subjected to an external harmonic force of amplitude is equal to 490 N and frequency is equal to 180 rpm. Find out force transmitted to the foundation.

Solution

It is given that

Mass = 120 kg

Stiffness = 2 × 106 N/m

F₀ = 490

ω= (2π 180)/60 = 6π r/s = 18.85 r/s

Frequency ratio r = ω /ω_n = 18.85 /40.82 = 0.4614

Force transmitted = F₀ ε

As damping is negligible.

∴             Force transmitted =490/1 - r ² = 1 - (0.4614)² = 622.5 N