4. Suppose two identical pendulums are coupled by means of a spring with constant k. See...
5. (Inhomogeneous equations: Laplace transforms: Resonance) A spring with spring constant k> 0 is attached to a m > 0 gram block. The spring starts from rest (x(0) - x'(0) 0 and is periodically forced with force f(t) - A sin(wft), with amplitude A > 0. (a) Write down the differential equation describing the displacement of the spring and the initial condition. (b) Solve the initial value problem from (a) using the Laplace transform. (c) What happens to the solution...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
Classical Mechanics problem: Consider the two coupled pendulums shown in the figure below. Each of the pen- dulums has a length L and the spring constant is k. The pendulums' position can be specified by the angles ¢\ and ø2. The relaxed length of the spring is such that the equi librium position of the pendulums is at ¢2 = 0 with the two pendulums vertical a.) Find the lagrangian L of this system. You can assume the angular deflections...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'(0)=x(0)=0 Find the solution of this differential equation using Laplace transforms. F(t) 7m The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1...
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)...
Thank you in advance Question: A mass weighing 4 N is attached to a spring whose constant is 2 N/m. The mass is initially released from a point 1 m above the equilibrium position and surrounding medium offers a damping force that is numerically equal to the instantaneous velocity. (a) Derive the system of differential equation describing the motion of the mass. (b) Find the equation of motion if the mass has a downward velocity of 8 m/s by using:...
NOTE: I need the correct answer with every single details The two coupled differential equations: *1 + 5x1 - 2x2 = 2e-t 32 - 2x1 + 2x2 = 0 Are subjected to initial conditions: x1(0) = 0 , x2(0) = 0 ,*1(0) = 0 ,*2(0) = 0 a) Find the laplace transform of the system and solve for X1(s) and X2(s). (2 points). b) Use MATLAB to find the inverse laplace transform. (2 points). c) Plot the solution from part...
(5 points) Suppose a spring with spring constant 6 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N.: ·s/m. a. Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of...
an object of mass "m" is attached to a spring with spring constant "k" and oscillated with simple harmonic motion motion. the maximum displacement from equillibrium is "A" and the total mechanical energy of the system is "ME." What is the system's potential energy when its kinetic energy is equal to 1/3 ME? (the answer should only have "k" and "A" as veriables, nothing else is allowed)