Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dax dx dt2 +3 + 2 x=0 with the following initial conditions: H *(0) = 1, (O) = vo, where v, is an unknown POSITIVE initial velocity of the cart. The value of v, must be found from the condition that the maximum of the displacement *(t) for positive t-values is equal to Calculate the required value of...
Problem #1 It is known that the displacement x(t) of a cart from the position of equilibrium is described by the mas spring model. The value of x(t) is the solution of the initial value problem as follows Calculate the mass m of the cart for which the maximum of the VELOCITY of the cart is equal to s. Round the value of the mass m you just found to three figures and provide your result below (16 points) (your...
Number 2 1. a) The displacement x of a forced spring-mass system is governed by dx d2x dt2 + (1 + t)x2 = sint t> 0 x(0) = 0 dx (0) = 0 dt dt Obtain the first four non-zero terms of the solution using the Taylor expansion approach. b) Calculate the position and velocity of the mass at t = 0.5 using the result of part (a). a) The displacement x of a forced spring-mass system is governed by...
Solve it with matlab 25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
A linear spring-mass system (without friction) satisfies m(d^2x/dt^2) = -kx, Derive that m/2 (dx/dt)^2 + k/2 x^2 = constant = E. Consider the initial value problem such that at t = 0, = x_0 and dx/dt = v_0. Evaluate E. Using the expression for conservation of energy, evaluate the maximum displacement of the mass from its equilibrium position. Compare this to the result obtained from the exact explicit solution.
I want matlab code. 585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is described by the following ordinary differ- ential equation: dx dx in dt2 dt where x displacement from equilibrium position (m), t time (s), m 20-kg mass, and c the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (underdamped), 40 (critically damped), and 200 (over- damped). The spring constant k-20 N/m. The initial ve- locity is...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey is changed...
a-d please 6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
An LTI system is described by the following differential equation. Find the output when x(t)- u(t) and has the following initial conditions: y(0)= 1, (0) = 2 , and x(0)--I dy x dx +at + 4 y(t) = dt + x(t) Solution