in undamped simple harmonic oscillator has mass 2.0 kg and spring constant 5 /m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the nitial velocity is 2.0 m/s. . From the initial conditions, determine the energy of the oscillator. Next, use th alue of the energy to determine both the displacement and velocity amplitudes. Determine and display the displacement in the form x(t) = Ccos(@ot + q), where s in meters and o is in radians.

Find the set of initial conditions such that each mass oscillates: a) at the first natural frequency; b) at the second natural frequency;

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A glider of mass 0.350 kg is placed on a frictionless, horizontal air track. One end of a horizontal spring is attached to the glider, and the other end is attached to the end of the track. When released, the glider oscillates in SHM with frequency 4.15 Hz. Find the period of the motion. Find the angular frequency of the motion. Find the force constant kk of the spring. Find the magnitude of the force that the spring exerts on the glider when the spring is stretched by 0.0200 m.

For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and equivalent damping coefficient when x (the displacement of the 2 kg block) is used as the generalized coordinate. b- Derive the equation of motion of the system in terms of equivalent system parameters (equivalent mass, equivalent spring stiffness and equivalent damping coefficient). 3000 N/m 2 kg 200 N.s/m /=0.04 kg-m² r = 10 cm 1000 N/m 1 kg I' 400 N.s/m ial

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;

ii. A mass spring system has three springs and mass m. Determine the equivalent spring stiffness, period and frequency of this system if the springs are connected in (a) series and (b) parallel. [Take the stiffness of the springs to be u, x and y and the equivalent stiffness as k]

The shafts shown have modulus of rigidity G1 and G2, derivethe differential equation of the system and determine the system naturalfrequency.

The mass of the system shown below is 10Kg. The mass is initially at rest when at time t=0, it is given an initial disturbance as shown. The viscous damping coefficient is 100NS/m and the spring stiffness, K is 100N/m. Which equation describes the movement of the mass. Disturbance Mass Spring Damper Select one: x(t) = (A, + A½t) e¯wnt a. %3D x(t) = A, e(-3+v?-1)wnt + A,e(-3-v?-1 )wnt x = (A3cos wat+ A4sin wat)e-wnt %3D C. Finish attempt.. evious page