An object attached to the end of a vertical helical spring bounces with a frequency of 2.1 Hz. If the spring constant is 5.9 N/m, what is the mass of the object?

A concrete part with a mass of 800 kg is hung on a 6 m long steel cable. You determine the spring constant to be 3.924 \times 10 ^ 6 N/m. What is the oscillation period when the steel beam oscillates in the direction of the cable? Provide the result in seconds.

A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator.  Find the damping ratio of the system  ζ . Find the transmissibility of the system,  Tf. Find the frequency ratio of the system, β.          Find the amplitude of the harmonic excitation force of the system,  Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X  in millimeters (mm).  Find the damped frequency of the system,  ωd  in rad/s. Find the force transmitted to the foundation,  FT  in Newton (N). Find the frequency of the harmonic…

Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping?  Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant.  Using c=5.0, what is the new period of oscillation.  What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.