4 HW_2nd ODE Application Part A) Mass spring damper system as represented in the figure. If...
. 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...
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...
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...
Please show work 3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
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.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the A second order mechanical system of a...
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,...
Thanks in advance 4. (8 points) We consider the mass-spring-dnmper systen in Figure &: A block af mes is saspended fron the eeiling by n spring with eonistant k nnd unstretched length lo and a damper with damping eoeficient d The block ean anly move vertienlly nnd its poesition is theresore fually deseribed by the z-courdinnte. An nlternative poeition is mensued from the statie rest position Furthermore, ngravitational neeclerstioa with mngnitude g is present. SYSTEM Fgure & A rigid body...
4. The two mass spring damper system below can be represented by the two differential equations TIR1 Since the system is represented by two second-order differential equations, find a fourth-order state- space representation, that is y=Cz + Du where A e R1x4, BE Rx, CERix4, and D Rx1. Use the state vector Hint: first, solve the first equation for , then replace by 21, by z2, and r2 by z3 as defined by matrix-vector form.