rad sec Using MATLAB, Plot x(t) for a damped system of natural frequency wn = 2 and initial conditions x0 = 1 mm, and vo = 1 mm for the following values of the damping ratio: = 0.01, 3 = 0.2, 3 = 0.1, 3 = 0.4, and 3 = 0.8.

Sketch frequency response of the system from part (a) in the form of Bode plot as accurately as you can.

A test was undertaken to find the dynamic properties of a SDOF system. The measured transient response recorded is shown in Figure QA2a. If the stiffness of the system is 1,000 N/m estimate: i) the damping ratio, ii) the undamped natural frequency, and iii) the mass of the system. Displacement (m) 0.08 0.06 0.04 0.02 O -0.02 -0.04 -0.06 -0.08 Figure QA2a 0.5 Time (s) 1.5 2

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An experiment was carried out on a SDOF system to estimate the natural frequency and damping. The time history plotted below has the response in centimetres and the time in seconds, as shown in Figure Q10 below. Estimate values for the following and choose the nearest values from the list given below: the damped natural frequency in Hz; the damping ratio using the logarithmic decrement method; and the natural frequency in rad/s. Ju(t) 2.00 AMA 1.00 0.00 0.00 Figure Q10 0.80 1.60 Select one or more: O a. 4.92 b. 0.781 c. 0.625 O d. 0.330 O e. 0.052 2.40 3.20 4.00 t

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solve, show solution and matlab code for plot, vibrations

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MA Figure (2) 3- The time response of a liner spring-mass-damper system with the mass of (m), the stiffness coefficient of (k), and a dampirg constant of (c) is given below in figure (2) with a set of coordinates marked by fillec circles. x(t) is in meters, it is in seconds. Indicate the units of all quantities involved in your solutions when calculate 0 -1- (0.53, 1.78) (0,0.8) 2 (2.1,-1.3) (3.7,0.9) L 4 (5.3,-0.7) - The damping ratio of the system. Its natural frequency w., damping corstart c, and stiffness coefficient k; for (m-1.25 kg). III- The amplitude of the motion if the phase angle is given as (0.4 rad). IV. Its initial conditions. (6.86, 0.5) 10 t[sec]

Find the Frequency Ratio, Displacement, Transmissibility Ratio, Absolute displacement of the mass, Type of Damping, and Equation of motion x(t). Assume Initial conditions for displacement and velocity. Graph 2 cycles of the vibrating system.