A 4-kg mass is attached to a spring with stiffness 12 N/m. The damping constant for the system is 8√/3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that i will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)

A 4-kg mass is attached to a spring with stiffness 12 N/m. The damping constant for the system is 8√/3 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that i will attain? The maximum displacement is meters. (Type an exact answer, using radicals as needed.)

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

Consider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?
A spring with a 8-kg mass and a damping constant 2 can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. Suppose the spring is stretched 1 meters beyond its natural length and then released with zero velocity. In the notation of the text, what is the value c2 – 4mk? m'kg/sec? help (numbers) Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form cieat cos(Bt) + cze"s t sin(&t) help (numbers) a = B = * help (numbers) * help (numbers) 8 = * help (numbers) C1 = help (numbers) C2 = 2 help (numbers) kies help us deliver our services. By using our services, you agree to our use of cookies. OK Learn more CONNECT OFF/ON CAPS Charge Po- 14 F4 F5 1- 1+ F6 F7 F8 F9 F10 F11 F12 7 8 R T Y U 5
A 10 kg vibrating system is placed on a table which is bolted to the floor. Due to operation of rotating equipment, the floor has a vibration amplitude of 0.2 mm at a frequency of 30 Hz. If the table is modeled as a spring of stiffness 1.3x106 N/m with a damping ratio of 0.04. Find the steady state acceleration amplitude of the vibrating system.
A body of mass 14 kg is suspended vertically on a spring and stretches it 49 cm. At t=0, the mass is released from a point 10 cm below its equilibrium position with an upward velocity of 15 cm/s and the subsequent motion takes place in a medium that offers a damping force numerically equal to twelve times the instantaneous velocity. Find the position function (the equation of motion) if the mass is driven by an external force f(t)=40cos(5t).
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 Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
3. A 3 kg object is attached to spring and will stretch the spring 392 mm by itself. There is no damping in the system and a forcing function of the form F(t) = 10 cos (17t) is attached to the object. If the object is initially displaced 20 cm downward from its equilibrium position and given a velocity of 10 cm/sec upward find the displacement at any time t. Show graph.
This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N-s/m The ball is started in motion with initial position to 9 m and initial velocity vo = -48 m/s. Determine the position function z(t) in meters. r(t) = Graph the function z(t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co S 38 E Co= Wo= (assume 0 do < 2π) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping. α0 =
A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…
A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 10 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s² for the acceleration due to gravity.) x(t) = ft
A mass m = 4 kg is attached to both a spring with spring constant k = 197 N/m and a dash-pot with damping constant c = 4 N-s/m. The mass is started in motion with initial position To = 2 m and initial velocity vo = 8 m/s Determine the position function z(t) in meters. r(t) = Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form z(t) = C₁e-pt cos(w₁ta₁). Determine C₁,w₁a₁ and p. C₁₂ = W₁ = -α₁ = P= Graph the function z(t) together with the "amplitude envelope" curves * = C₁e-Pt and x = C₁e-pt Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0) Solve the resulting differential equation to find the position function u(t). n this case the position function u(t) can be written as u(t) = Cocos(wotao). Determine Co, wo and co Co Po (assume 0 a₁ < 2π) 20 (assume 000 < 2π) inally graph both function (t) and u(t) in the same window to illustrate the effect…
Q3/ For the system shown in figure if the damping ratio is 0.3 derive the equation of motion using Newton's second law and find: a- The natural frequency. b- The damping constant. c- The ratio of any consecutive cycles. k=2 x 10 N/m m = 4.2 kg 10 cm 40 cm 60 cm ITTTI
Shock absorber. What is the smallest value of the damping constant of a shock absorber in the suspen- sion of a wheel of a car (consisting of a spring and an absorber) that will provide (theoretically) an oscillation- free ride if the mass of the car is 2000 kg and the spring constant equals 4500 kg/sec²?