A 600-kg machine is mounted on a rigid floor of a factory through a spring of stiffness 1,500,000 N/m and a dashpot with unknown damping coefficient. The machine produces a constant harmonic force of 500 N. When the machine operates at 100 rad/s, its steadystate displacement amplitude is observed to be 0.0001 m. (a) Determine the damping coefficient of the dashpot, and compute the phase angle between the force and displacement at 100 rad/s. (b) Compute the values of the system’s undamped natural frequency, critical damping coefficient and damping ratio (c) Determine the velocity and acceleration amplitudes of the machine at 100 rad/s. (d) Evaluate the percentage change of the steady-state displacement amplitude and phase of the machine if the frequency is now increased to 150 rad/s.
A 600-kg machine is mounted on a rigid floor of a factory through a spring of stiffness 1,500,000 N/m and a dashpot with unknown damping coefficient. The machine produces a constant harmonic force of 500 N. When the machine operates at 100 rad/s, its steadystate displacement amplitude is observed to be 0.0001 m.
(a) Determine the damping coefficient of the dashpot, and compute the phase angle between the force and displacement at 100 rad/s.
(b) Compute the values of the system’s undamped natural frequency, critical damping coefficient and damping ratio
(c) Determine the velocity and acceleration amplitudes of the machine at 100 rad/s.
(d) Evaluate the percentage change of the steady-state displacement amplitude and phase of the machine if the frequency is now increased to 150 rad/s.
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