An undamped single-degree-of-freedom system consists of a spring with stiffness k = 10 kip/in and a mass weighing W = 10 kips. The system is at rest and it is suddenly subjected to a half-cycle sine pulse force. The pulse force has an amplitude po = 1 kips and time duration td = 0.1 seconds. Calculate the maximum restoring force in the spring due to the pulse force.

Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?

8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use g = 9.8 m/s²) Sol.

Derive the governing equation of motion of the mass-spring system on an inclined plane as shown in the figure below. Then determine the natural frequency of the given system. Please remember to state all assumptions and include a free-body diagram. ki ww k: m www A

Mohammed Mahad Tabook A lathe can be modeled as an electric motor mounted on a steel table. The table plus rotor have a mass of 100 kg. The rotating parts of the lathe have a mass of 10 kg at a distance 0.1 m from the center. The damping ratio of the system is measured to be zeta= 0.06 (viscous damping) and its natural frequency is 7.5 Hz and the driving frequency is 30HZ The natural frequency in rad/s is Choose.. The driving frequency in rad/s is Choose... The frequency ratio is Choose... The amplitude of the steady-state displacement of the motor (in mm) Choose... the phase shift of the steady state displacement (in rad) is Choose... +

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A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is released from a point 10 cm below its equilibrium position with an upward velocity of 15 cm/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to twelve times the instantaneous velocity. Find the position function (the equation of motion) if the mass is driven by an external force f(t)=40cos(5t).

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 F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s

Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b

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