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(1 point) This is an example of an Undamped Forced Oscillation where the phenomenon of Beats...
could someone explain this with helpful workspace? Problem 3. (1 point) Use the Laplace transform to solve the following initial value problem: y" +9y' = 0 y(0) = 3, y(0) = 5 a. Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation 0 b. Now solve for Y(S) = c. Write the above answer in its partial fraction decomposition, Y(s) = sta +...
Problem 1.Consider the harmonically forced undamped oscillator described by the following ODE:mx′′+kx=F0cosωt, k >0, m >0, ω >0, F0∈R. Problem 1. Consider the harmonically forced undamped oscillator described by the following ODE: mx" + kx = Fo cos wt, k > 0, m > 0,w > 0, F0 E R. (1) a) Suppose wa #k/m. Find the general solution of the ODE ). b) Consider the initial value problem of the ODE () with initial conditions x(0) = 0 and...
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0 2 (a) Determine the natural frequency of the unforced system (b) Find the solution (t) forw1 (c) Plot the solution x(t) versus t for w = 0.7, 0.8, and 0.9. (Feel free to use technology. MatLab, Mathematica, etc.) Describe how the response (t) changes as w varies in this interval. What happens as w takes values closer and closer to 1? Briefly explain why...
10. Consider the forced but undamped system described by the initial value prob- lem u" + 25u = sin(wt), (0) = 0, ta (0) =1. a. Find solution for u(t) when w #5. b. Plot the solution u(t) versus t for w = : 4, 4.5, and 4.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 5? Note that the natural frequency of the system is wo = 5. (Hint: Make the...
3. Consider the forced but undamped system described by the initial value problem u" +u = 3 cos(wt), 4(0) = 0, 1'0) = 0. a. Find solution for u(t) when w 1. b. Plot the solution u(t) versus t for w = 0.7, 0.8, and 0.9. Describe how the response u(t) changes as w varies. What happens when w gets close to 1? Note that the natural frequency of the system is wo = 1.
#40 a-f B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Differntial Equations Forced Spring Motion 1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
Problem 2. Recall that any undamped spring-mass system is described by an initial value problem of the form m" + ky= 0, (0) = 0, v(0) = to, where m is the mass and k is the spring constant. Since there is no damping, we would expect that no energy is lost as the mass moves. That is, the total energy (potential plus kinetic) in the system at any time I should equal the initial amount of energy in the...
(1 point) This problem is concerned with solving an initial boundary value problem for the heat equation: (0,t)-0, t0 u,o)- in the form, ie where the term involving cy may be missing. Here y is the eigenfunction for Ay- 0 so if zero is not an eigenvalue then this term will be zero First find the eigenvalues and orthonormal eigenfunctions for n1.iA. Pa(x). For n 0 there may or may not be an eigenpair. Give all these as a comma...