Question

A machine of mass m= 500 kg is mounted on a simply supported steel beam of length l=2 m having a rectangular cross-section (depth = 0.1 m, width = 1.2m) and young's modulus E = 2.06 * 10^11 N/m^2. To reduce the vertical deflection of the beam, a spring of stiffness k is attached at mid-spam, as shown in fig. Determine the value of k needed to reduce the deflection of the beam by A) 25% of its original value. B) 50% of its original value. C) 75% of its original value.
Assume that the mass of the beam is negligible.