11. In the spring-mass-damper system shown in the diagram below, the mass is regarded to be negligibly small. The system is disturbed by an external force which leads to the simplified first degree differential equation d+ y =!1 where n is the damping constant and k the spring constant and y is the displacement of the mass dtn from its equilibrium. Solve this differential equation if it is known that y(0) = 0. Present your solution with y as the subject. Determine the steady state of y. Hint: Since k and n are constants, let = M and != N, that is, solve + My = Nt. dt Dinube Spag Deper

11. In the spring-mass-damper system shown in the diagram below, the mass is regarded to be negligibly small. The system is disturbed by an external force which leads to the simplified first degree differential equation d+ y =!1 where n is the damping constant and k the spring constant and y is the displacement of the mass dtn from its equilibrium. Solve this differential equation if it is known that y(0) = 0. Present your solution with y as the subject. Determine the steady state of y. Hint: Since k and n are constants, let = M and != N, that is, solve + My = Nt. dt Dinube Spag Deper

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

4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.
Find the response of the mass if it is subject to the force in the plot. The damping ratio for the system is 0.1. You do not have to expand the series nor carry out any multiplication in the response equation. Hint: ao = 0. You may use this value and do not have to calculate ao- 2a 50 Mass m m = 10 kg Massless Rigid Rod a =0.3 m Massless Circular Cord -50 Length { = 0.625n m Diameter d = 0.01 m 0 1 Time (s) -2 -1 2 3 Modulus E = 0.001 GPa Force (N)
A mass m = 4 kg is attached to both a spring with spring constant k = 101 N/m and a dash-pot with damping constant c = 4 N. s/m. The mass is started in motion with initial position xn = 5 m and initial velocity vn = 3 m/s Determine the position function x(t) in meters. x(t) Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form æ(t) = Cje pt cos(wit – a1). Determine C1, wi ,ajand p. C = (assume 0 < aj < 27) p = Graph the function x(t) together with the "amplitude envelope" curves a = -Cje-pt and r = Ce-pt Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( soc = 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(wat – ao). Determine Co, wo and aæn. Co = wo = (assume 0 < an < 27 ) Finally, graph both function x(t) and u(t) in the same window to illustrate the…
Suppose a weight of mass 5 kg is attached to a spring with spring constant k = 5 N/m and damping constant c = 10 Ns/m. At t=0 the mass is 0.1 m below its equilibrium position with velocity 0.2 m/s toward the equilibrium position. How many times will the mass return to its equilibrium position? Hint: either never, once, or infinitely many times.
Solve in good image
3. The Duffing equation describes a nonlinear oscillator with a nonlinear spring (energy storage component) and possibly a damping component: equation. m i d²x dt2 2 +c dx + kx + εx³ = f(t), where c, k and & are constants. dt Chow that the Duffing equation fails to meet the requirements for a linear operator Develop the general solution for the case where & =0 and f(t) = 0, and the initial conditions are x(0) = xo, dx/dt(0) = vo; and show why the approach will not work for the case when �. For the case where c = 0 and f(t) = 0, the homogeneous DE falls into one of the categories of second order ODE's that can be integrated using a transformation of variables. Using that transformation, carry the solution process as far as you can.
solve using laplace
A mass weighing 1/4 kg. is attached to a spring with stiffness k = 16 N/m. The mass is displaced 1/2 m. to the right of the equilibrium position and given a rightward velocity of 1 m/sec. Neglect damping and external forces. Find y(t), A, phi, omega, the period P and the first time (t>0) the mass passes through equilibrium.
Q. 22: Determine the mass as a function of time for the system given below. g Figure 6
4- The logarithmic decrement can be obtained as & In*, is it possible to get a negative value of 8 when the system is damped (3 < 1)? Why?