1- Consider a spring mass system shown below with K = 8N/m and m= 9kg. It's...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
Please write legibly Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
For the spring-mass system shown below with the mass sliding on a frictionless floor, A = 1.0 m, the spring constant k = 2.0 N/m, and the mass m = 2.0 kg. The period of oscillation T is QUESTION 18 For the spring-mass system shown below with the mass sliding on a frictionless floor, A = 1.0 m, the spring constant k = 2.0 N/m, and the mass m = 2.0 kg. The period of oscillation T is x= 0...
F(t) 1. The spring-mass system shown in the figure has • m=40kg, • k = 38.6kN / m • C=0.2518kNs / m The mass vibrates harmonically with an amplitude of 1mm and angular frequency @=100rad /s . 1.1 What is the amplitude of the force? 1.2 What is the frequency of the force that yields the maximum vibration amplitude? If the force amplitude is the same as the value computed in 1.1, what is the resulting vibration amplitude?
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
Consider a vertical mass-spring system. The spring constant is k = 48N the mass is m = 1.0 kg. (a) Find the angular frequency. The mass is pulled from equilibrium 0.10 m down. (b) Write the equation for the displacement as a function of time, with a vertical xaxis pointing upward.
A system made up of a mass (m), attached to a spring of stiffness k [N/m] will oscillate to a specific amplitude (A) which will depend on an external force (F) and initial conditions. If all the variables involved are given in Table 1, formulate the necessary Pi groups to describe this behavior. Make sure you write the Pi groups using the parameters involved Parameter Variable Variable Units Amplitude A т Mass m kg Spring k N/m constant External F...
Question (b) Ans : root(7/2) , 16/((5)^(1/2)) 9. Consider a mass-spring system as shown in the figure with a body of mass m, a spring and a dashpot. Let k, c and r(t) be the spring constant, the damping constant and driving force, respectively Let y(t) be the displacementMass of the body from the equilibrium with downward direction as positive. b) [7pts] Let m=1, c=1, k=4, and r(t) 8cosut. Determine w such that you get the steady-state vibration of maximum...
Consider the spring-mass-damper system shown. Assume M-1kg. B - 20 N-s/m, K-25 N/m and f(t) = ON (zero-input case). The initial conditions are: x(O) = 1 m, x(0) = 0 m/s Select the correct plot of "x vs. t" for this zero-input case. They M B 0 0 O O o
(a) Find the period of oscillation for a spring-mass system where the spring constant (k) is 24 N/m and the mass (m) is 6 kg. (b) Write an equation for x(t) if the spring is stretched to an amplitude of 10 cm from its equilibrium position x = 0 at t = 0. (c) Write an equation for the following initial conditions: at t = 0, the mass is at x = 0 and has a velocity of +3 cm/s.