spring-mass-damper Q3) For the system shown to the right, x is measured from the static equilibrium position, and the surface is frictionless. Determine the equations of motion, period and damped of each oscillation If the system is released with the initial conditions: x(0) = 0.0 m, x (0) = 5.0 m/s, find the resulting solution x(t) if m= 2 kg, k = 48 N/m and c = 4 N/(m/s). St 171

spring-mass-damper Q3) For the system shown to the right, x is measured from the static equilibrium position, and the surface is frictionless. Determine the equations of motion, period and damped of each oscillation If the system is released with the initial conditions: x(0) = 0.0 m, x (0) = 5.0 m/s, find the resulting solution x(t) if m= 2 kg, k = 48 N/m and c = 4 N/(m/s). St 171

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Q3: The response for the system shown is given by the plot of x(t) vs t. If the spring constant is (k = 100 N/m) Find: The initial velocity of the mass m? Step Response x(1) m
Clear selectior A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with an amplitude A = 0.1 m. At what position (x = ?) would the kinetic energy of the system be equal to three times its elastic potential energy (K = 3U)? %3D At x = +0.05 m At x = +0.04 m At x = +0.025 m At x = +0.08m At x = +0.1 m A traveling wave on a taut
3. A 100-pound weight is suspended from a vertical spring whose module is 100 pounds per foot. The weight is pulled downward 9 inches from its equilibrium position and released. Viscous fluid exerts 20 Ibs of force when the plunger moves through it at 0.5 ft/sec; 3.a What is the damping condition? Write the equation which describes the motion of the weights. Show graph. 3.b displacement 3.c velocity 3.d acceleration
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of F friction We can write the resulting system of second-order DEs as a first-order system, w'(t) = Aw(t), with w = (x₁, x₁, x₂, x₂) T For values of k = 4, m = 1 and c = 21,2 = 0.5±3.2i, V₁ 23,4= - 0.5 ± 1.13i, V3 1, the resulting eigenvalues and eigenvectors of A are -0.039 0.248i 0.813 0.024 +0.153i -0.502 -0.134-0.302i' 0.409 -0.216 - 0.489i 0.661 and (a) Find a set of initial displacements x₁(0), x₂(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. (x₁(0), x₂(0)) Enter your answer using angle braces, (and ). cx (friction proportional to velocity). (b) At what frequency will the masses be oscillating in this mode? Frequency = rad/s
Q2\ The period of damped linear oscillation for a certain 1 kg mass is o.32 sec. If the stiffness of the supporting linear spring is 850 N/m, calculate the damping coefficient C and the critical value C, of the motion.
F(1) Spring m. Ball Dashpot Find the motion of the mass-spring system with the driving force F(t) shown above for the given data. [Hint: Read Forced Oscillations notes.] e-2t, 0 2 y(0) = 1, y'(0) =-1.5.
For the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k = 2 N/m and f(t) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) Find the steady state maximum acceleration.
3) Here is a simplified model of vehicle suspension system. The vehicle is being driven on the road below. The profile of the road and the velocity of the car in the horizontal direction are given. A road with such a profile will create an oscillation in the body of the car (the oscillation is denoted by y(t)). 1 y 1) Please obtain the magnitude of y(t) as a function of k and c. 2) Assume the mass of the car as 1 kg, k=10 N/m and c=2 Ns/m. What should the velocity of the car be to make ly(t)| less Vx = 3 m/s than 0.001 m? X : horizontal distance in meters sin(4x) the profile of the road in meters
A mass weighing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 8 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to - the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 25 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ft
4) Consider the following mass spring damper system: m2 u(t) Assuming that y, > y1, equation of motion (EOM) for this system can be obtained by applying the Newton's second law: = mỹ (i. e. RHS is positive) Then, equations are written as: m,y, = k2(y2 – Yı) – kıyı – cỷı (1) m2yz = u(t) - k2(y2 - Yı) (2) where u(t) is the input function to the system. Take m, = 1 kg, m2 = 2 kg, c = 10 Ns/m and k = 10 N/m, k2 = 20 N/m. Then, answer the following questions. ¥½(s) a) Find the transfer functions G, (s) = 1 and G2(s) = U(s) U(s) b) Use Laplace transform method and obtain the displacements in Laplace space (i.e. s domain) Y,(s) and Y2(s) utilizing initial conditions y, (0) = 0, y2(0) = 1, ỷ, (0) = 1 and y2(0) = 0. Use Cramer's rule for the solutions of Y, (s) and Y2(s). c) Using Inverse Laplace transformation, obtain displacements in time space (i.e. time domain) Y1(t) and y2(t) if, c.l. u(t) = 8(t) (Impulse function) (Ramp function starts from t=2) c.2. u(t) = {"2, 2st<∞ 0, 0st< 2 u(t) t-2 O…
The period Ta of damped linear oscillation for a certain 1 kg mass is 0.27 s. If the stiffness of the supporting linear spring is 800 N/m, calculate the damping coefficient c. Insert your answer for c in N. s/m correct up to at least a third decimal place.
Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b