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 stif...
4 HW_2nd ODE Application Part A) Mass spring damper system as represented in the figure. If the block has a mass of 0.25 (kg) started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of 4 (N/m) and the damping coefficient C (Ns/m) such that c is less than 4 Ns/m. Find all possible equations of motion for the block. k 772 TH Part B) If a two DC motors applied an external...
. Shies Paragraph HW 2-ODE Application Part Al Mass spring damper system as represented in the figure. If the block has a mass of 0.25 g started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of (N/m) and the damping coefficient ciNs/m such that is less than 4 Na/m. Find all possible equations of motion (t) for the block Part If two DC motors applied an external force (t) = n(t) and...
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.
63 Figure P6.3 shows a mass-damper system (no stiffness, Problem 2.3). Displacement x is measured from an equilibrium position where the damper is at the "neutral" position. The external force () is a short-duration pulse function: f(!)-5N for 0SS002 s, and f,() = 0 for t > 0.02 s. The system parameters are mass m-0.5kg and viscous friction coefficient b 3 N-s/m and the system is initially at rest. Usc Simulink to determine the system response and plot displacement xit)...
1. Given the spring-mass-damper system in the figure below T3 T1 T2 b2 b1 k3 (a) Find the equations of motion for each of the masses 脳. Fi(s) (b) Assume F1 0 and find the transfer function (c) Assume Fs 0 and find the transfer function (d) Write the equations in matrix-vector form: M.ї + Bi + Kx-F where z is a 3 x 1 vector with the displacements r,2, r3 as components, M is the mass matrix, B is...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
Problem 1: For the system in figure (1-a), the spring attachment point B is given a horizontal motion Xp-b cos cut from the equilibrium position. The two springs have the same stiffness k 10 N/m and the damper has a damping coefficient c. Neglect the friction and mass associated with the pulleys. a) Determine the critical driving frequency for which the oscillations of the mass m tend to become excessively large. b) For a critically damped system, determine damping coefficient...
A 1-kg mass is attached to a spring with stiffness 45N/m. The damping constant for the system is 6 N-sec/m. The mass is pulled 1 m to the right of the equilibrium position and released. Find the equation of motion in phase-shift form. When will the mass first return to its equilibriom position, and at what velocity? A 1-kg mass is attached to a spring with stiffness 45N/m. The damping constant for the system is 6 N-sec/m. The mass is...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (b)...
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...