Consider the damped mass-spring system for mass of 1.5 kg, spring constant 10 N/m, lamping 3 kg/s and an oscillating force 4.7 cos(@t) Newtons. That is,

A h HU y h An object of mass 0.3 kg is released by pushing down a little (y) while floating with h-20 cm submerged in water. a) Write the differential equation of the free oscillations of the system, assuming that, during the motion, the body is subjected to a damping force given by -bv (v is the velocity of the body. b is the damping constant). b) If the frequency of the damped harmonic motion is half the frequency when there is no damping, what is the value of the damping constant?

1. ooo 1 B₁ M₁ पती System coefficients: K₁ = 600 N/m K₂ = 400 N/m C₁ = 8 kg/s C₂ = 2 kg/s M = 50 kg K₂ 000 -fa(t) x2 M₂ B₂ Figure P2.1 Determine the free-body-diagram of the system above. Derive the equation of motion (EOM).

PART OF MECHANICAL VIBRATIONS SUBJECT USE VIRTUAL WORK   The uniform bar shown in Fig. P3.6 has mass m, length l, and mass moment of inertia 1 about its mass center. The bar is supported by two springs kı and k2, as shown in the figure. Obtain the differential equation of motion and determine the natural frequency of the system in the case of small oscillations.