A 2-kg mass is attached to a spring with stiffness 10 N/m. The damping constant for the system is 4√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 2 m/sec, what is the maximum displacement from equilibrium that it will attain?

Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s

A 2.50-kg object is attached to a spring with a force constant of 4.50 N/m. The object rests on a horizontal surface that has a viscous, oily substance spread evenly on it. The object is pulled 15.0 cm to the right of the equilibrium position and set into harmonic motion. After ?1=2.00 s the amplitude has fallen to 7.00 cm due to frictional losses in the oil. Calculate the damping constant ? for the oil.

19. A weight of 25 N is suspended from a spring that has a stiffness of 1,000 N/m. The weight vibrates in the vertical direction under a constant damping force. When the weight is initially pulled downward a distance of 10 cm from its static equilibrium position and released, it comes to rest after exactly two complete cycles. Find the magnitude of the damping force.

A 2-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.5 m and reaches a maximum speed of 2 m/s. What is the spring constant in N/m?

A 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.3 m and reaches a maximum speed of 5 m/s. What is the spring constant in N/m?

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.

Suppose a weight of mass 5 kg is attached to a spring with spring constant k = 5 N/m and damping constant c = 10 Ns/m. At t=0 the mass is 0.1 m below its equilibrium position with velocity 0.2 m/s toward the equilibrium position. How many times will the mass return to its equilibrium position? Hint: either never, once, or infinitely many times.