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1. a) The displacement x of a forced spring-mass system is governed by dx...
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 #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 dx dx + 2x 0 +3 dt with the following initial conditions: x (0)1 where to is the unknown POSITIVE initial velocity of the cart. The volue of must be found from th condition that the maximum of the dixplecement x(e)for ositive tvoles is equel to 2 (0)o Calculate the required value of , round it off to...
I want matlab code. 585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is de...
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...
A linear spring-mass system (without friction) satisfies m(d^2x/dt^2) = -kx, Derive that m/2 (dx/dt)^2 + k/2...
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.
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following seco...
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
SOLVE NUMERICALLY USING EULERS METHOD
The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: m d2x dt2 1 c dx dt 1 kx 5 0 where x 5 displacement from equilibrium position (m), t 5 time (s), m 5 20-kg mass, and c 5 the damping coeffi cient (N ? s/m). The damping coeffi cient c takes on three values of 5 (underdamped), 40 (critically damped), and 200 (overdamped). The spring constant k 5 20 N/m. The...
A mass weighing 8 pounds lengthens a spring by 2 feet assuming that a damped force...
A mass weighing 8 pounds lengthens a spring by 2 feet
assuming that a damped force equal to 2 times the instantaneous
velocity and acting
on the system determines the equation of motion if the initial mass
is released from the equilibrium position with a velocity ascending
3 ft / s. Solve the previous exercise with La Place transforms
m d2x dx + B + kx = 0 dt dt m = 0.25 pulg k = 4 lb/ft B =...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m-...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m- 1 kg, c 1 N-s/m, k = 1 N/m, and f(t)-1 N for all time. If the initial displacement and velocity of the mass are zero, then based on the central difference numerical integration method as discussed in the notes, using an integration time step of h 0.5 s, what is the displacement of the mass at t 0.5 s? In other words, what...
2. Consider the mass-spring system shown in the figure below. It can be shown that the...
2. Consider the mass-spring system shown in the figure below. It can be shown that the motion of the mass is governed by the equation a=-sw^2, where s and a are the position and acceleration of the mass, respectively, and w is a constant (which is referred to as the natural frequency of the system). Derive the equation describing the velocity of the mass in terms of the position. Assume that the velocity of the mass is v(subzero) when s=0...
Solve it with matlab 25.16 The motion of a damped spring-mass system (Fig. P25.16) is described...
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....
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 #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dx dx + 2x 0 +3 dt with the following initial conditions: x (0)1 where to is the unknown POSITIVE initial velocity of the cart. The volue of must be found from th condition that the maximum of the dixplecement x(e)for ositive tvoles is equel to 2 (0)o Calculate the required value of , round it off to...
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...
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.
3. The motion of a 1DOF mass-spring-damper system (see Figure 1) is modeled by the following second order linear ODE: dx,2 dt n dt2 (0) C dt where is the damping ratio an wn is the natural frequency, both related to k, b, and m (the spring constant, damping coefficient, and mass, respectively) (a) Use the forward difference approximations of (b) Using Δt andd to obtain a finite difference formula for x(t+ 2Δ) (like we did in class for the...
A mass weighing 8 pounds lengthens a spring by 2 feet
assuming that a damped force equal to 2 times the instantaneous
velocity and acting
on the system determines the equation of motion if the initial mass
is released from the equilibrium position with a velocity ascending
3 ft / s. Solve the previous exercise with La Place transforms
m d2x dx + B + kx = 0 dt dt m = 0.25 pulg k = 4 lb/ft B =...
For the single DOF spring-mass-damper system shown, the displacement of the mass is x. Assume m- 1 kg, c 1 N-s/m, k = 1 N/m, and f(t)-1 N for all time. If the initial displacement and velocity of the mass are zero, then based on the central difference numerical integration method as discussed in the notes, using an integration time step of h 0.5 s, what is the displacement of the mass at t 0.5 s? In other words, what...
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....
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