A 0.31kg block rest on a orizonal surface and is attached to a spring (constant=41 N/m ). The block is initially moved 9cm from equillibrium position and is released. As the block oscillated, there is a frition force of 0.4 N between the oscillating block and surface. Calcualte the block's speed web it goes through the equilibrium pasiotion after ebing released from 9-cm desplacement pint, Assume the block underges simple harmonic motion. 0.681 m/s 2.266 m/s 0.916 m/s 1.034 m/s none

When spinning at 500 rotations per minute two washing machines produce two sinusoidal forces with same maximum amplitude of 400N, but their maximum amplitudes are separated in time by 0.0125s. The two machines are placed side by side and to check their effect on a suspended laundry floor it is necessary to find their resultant vertical force. Find time-varying function describing the resultant of the two vertical forces including the amplitude and phase shift relative to one of the two excitation forces.

14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;

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

An undamped free vibration system consisting of mass m = 5 kg and stiffnessa spring of 400 N/m, is given an initial displacement of 0.02 m and is kicked with an initial velocity of 0.1 m/s.Determine the equation of motion for the system.

A factory machine with a mass of 320 kg vibrations up and down with frequency of 8 Hz. Amplitude of engine movement of 2 mm. Calculate the maximum acceleration of the machine, and what is the maximum Newtonian force obtained?

A mass weighing 16 pounds stretches a spring 4 feet. The mass-spring system is submerged in a liquid that imparts a damping force numerically equal to 3 times the instantaneous velocity. The mass is initially released 2 feet below the equilibrium position with an downward velocity of 6 ft/sec. Find the equation of motion

Ex. A vehicle wheel, tire and suspension assembly can be modeled crudely as a single degree of freedom spring mass system. The mass of the assembly is measured to be about 300kg. its frequency of oscillation is observed to be π rad/sec. What is the approximate stiffness of the tire, wheel and suspension assembly? ilippines) Accessibility: Investigate