A machine with a mass of 250 kg is placed on isolator and the corresponding free vibration records is as shown in Figure. Determine the type of damping, its stiffness and damping constant. Consider the first 2 cycles. x(t) 0.01 0.008 0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 0 0.5 1 1.5 2 2.5 3 3 t 3.5

(a) The position-time plot of a spring-mass-damper system is as shonn Find the damped frequency. Find the logarithmic decrement. Find the damping ratio. Spring Mass Damper 12 Time Position

Can you please show the complete solution of the image below. Thanks! Subject: Mechanical Vibration

Please answer question number 3

A mass-spring system is driven by the external force g(t) = 2 sin3t + 10 cos 3t. The mass equals 1, the spring constant equals 5, and the damping coefficient equals 2. If the mass is initially located at y (0) =-1, with initial velocity y' (0) = 5, find its equation of motion to find y (1). Round up the answer to the second decimal place point.

The graph shows the displacement versus time of a mass in a mass-damper-spring system. Which of the following could be the damping ratio of the system? x(t) in 0,5 O 0.65 O 0.38 O 1.22 0.12 1.5 t 20

1 Free Vibration Response of Single Degree of Freedom System(100 %) Figure 1 represent a simple vibration system. The free vibration response of an undamped single degree of freedom (SDOF) oscillator is given by its displacement x(t) satisfying x(t) = x(0)sin*(wt)e-2dwt + v(0) (1) -cos(wt)e-10dwt %3D where t is time in seconds and w = Vis the natural frequency of the system with m and k being the mass and the stiffness of the system. d is the damping coefficient of the system. Define v(t) and a(t) as the time dependent velocity and acceleration of the system. Write an M-file script using functions that will compute and plot 1. The displacement of the system x(t) over time 2. The velocity of the system v(t) over time 3. The acceleration of the system a(t) over time for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10 s. You will need THREE(3) functions, one for each displacement, velocity and acceleration calculations. Assume m = 10, k = 1 and that r(0) = v(0) =…

The answer should be in Handwritten format.

Select the right answer for each of the following: 1- The damped vibrational system is. system, (c) none of these, (d) false statement. (a) conservative system, (b) nonconservative (a) viscous (b) solid 2- When a system vibrates in a fluid medium, the damping is (c) Coulomb. 3- When an initial excitation exerted on a vibrational system results in - ippearance. (a) natural frequency. (b) resonance. (c) beating. (d) none of these. 4- Undamped vibration is characterized by no loss of 1) (a) speed, (b) acceleration, (c) mass, (d) energy. (a) mass, (b) damper, 5- Vibratory system should at least consists of a spring and - (c) mass and damper.

4. A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T 2π Wd According to (4), show that the logarithmic decrement dis T = x1 8 = log = x2 where log has base e. Combine (5), (7), and (8) to obtain = (WnT 8 4π² +8² Will this method work for other initial conditions? why?