A mass of 8.0 kg oscillates at the end of a spring of stiffness 28.3 Nm-¹. If the damping ratio is 0.3, determine the damped natural frequency in rad/s. (Express answers to 2dp)
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- A mass of 7.9 kg oscillates at the end of a spring of stiffness 26.1 Nm-¹. If the damping ratio is 0.2, determine the damped natural frequency in rad/s. (Express answers to 2dp) Answer:An advertisement board was pulled from the top point with a horizontal force of 100 kN with the help of a jack and subjected to 75 mm horizontal displacement. when the force is released suddenly, the time elapsed at the end of the 5th oscillation was measured as 1.50 seconds and the amplitude as 30 mm. 75 mm a ) Find the damping ratio of the system. b ) Find the natural vibration period Tn of the system and the damped period Td of the system. c ) Find the horizontal translational stiffness of the system.A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1 b.0.7 c.0.9 d.0.8 2)Calculate the magnification factor (M) of the system. a.0.86 b.1.25 c.0.312 D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters). a.0.2 b.0.1 c.0.4 D.0.3
- An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50 N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the initial velocity is 2.0 m/s. %3D 1. Determine the angular frequency (in rad/s), the frequency (in Hz), and the period (in s). Determine numerical values (not in terms of .) Determine the displacement in the form x(t) = Acos(mot) + Bsin(@ot). That is, solve for A and B in meters, and write oo in radians per second.2- A free vibrations test is run to determine the stiffness and damping properties of an elastic element. A 20 kg block is attached to the element. The block is displaced 1 cm and released. The resulting oscillations are monitored with the results shown in Figure (1). Determine k and c for this element. 0.01 0.008 0.006 0.004 0.002 0 -0.002 -0.004 -0.006 -0.008 -0.01 0 0.06 0.12 0.18 Figure (1) 0.24 0.30 0.3A mass of 10kg oscillates at the end of a spring of stiffness, 5N/m. If the damping in the system is such that it gives a damping ratio of 0.45, determine. i) The critical damping. ii) The value of the damping coefficient. iii) The damped natural frequency. iv) The equation for the displacement if the initial velocity is 0.025m/s, and the initial displacement is 0 m.
- The mass of a single degree of freedom damped vibrating system is 75 kg and vertically attached to the spring of a stiffness 10.5 kN/m as shown in Figure 2. The damping coefficient of the system is 600 Ns/m and the system is excited by a force: F=700sin25t in Newtons and t-is the time in seconds 2.1 Calculate the natural frequency of the system in rad/s 2.2. Calculate the periodic time of the system if at free vibrating mode and that of exciting force.2.3. Using the damping ratio criteria, state the damping type of the system. (5)A single degree of freedom system with mass of 100 Kg, a damping ratio of 0.707 tf and a natural frequency of 8 HZ. The base of the system is excited with a frequency of 80 rad/s, The natural frequency of the system in rad/s Choose... is The value of the stiffness of the system is (N/m) Choose... The damper of the system (in kg/s) is Choose... The frequency ratio is Choose..The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system. Note: Give your answer to 3 decimal places. Other Parameters: Logarithmic Decrement (8): Answer: 2ng 2T C 8 = In = In1 = 5 wnTd = 5wn X2 Xn+1 1-5 wa 2m k Damping Ratio (5): 5= 2vkm 2mn V(21)2+8 Frequency of damped vibration (wa): wa = 1-Wn Undamped Forced Vibration: Frequency Ratio (): r- Xp-x sin w t Next page Hous page Type here to search
- 1. Suppose you are riding your bicycle on a bumpy road having a surface profile that varies harmonically with +/- 6 cm undulations. The distance between consecutive peaks of these undulations is 2 m. When you sit on the seat of your bike for your casual ride, the springs deflect 5 cm. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. (a) If you are riding your bicycle at a horizontal speed of 2.5 m/sec, how much bumping up and down will you experience? (b) Next day, you are carrying a backpack which increases your on-seat weight by 20%. Assuming that you are still able to ride with same speed, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? M k/23 k/2 6 cm 2 mQI: A portion of an automobile suspension system consists of an elastic spring and a viscous damper, as shown. If the natural frequency is 10 rad/sec, a) Determine the damping ratio so that any oscillations that occur will decay from 11-0.5 m to x2-D 0.025 m. b) If the system is displaced 0.2 m from its equilibrium position, and released from rest, determine the position of the mass after it has ascillated through 3 cycles.*Hi, please help me with this differential equations questions and please show the full solution. Thank you very much. * Question 1.) A load weighing 2 kg is attached to a spring. If the damping force is 5.5, spring constant is 4.2, and external force is sin(t), and the load is released from rest 0.2 inches below its equilibrium, determine the displacement of the object at any time t.