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Dynamical systems have been a research topic since newton's time due to their significant role in the sciences. Dynamical systems answer many questions like, How does the solution behave as time goes to infinity? Describe turbulence. System dynamics engineering courses emphasize hands-on learning and a strong mathematics foundation. Due to it, most students need homework help but can’t find a reliable service. TutorBin's tutors provide the best system dynamics solutions to aid those students.

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TutorBin: No.1 Online System Dynamics Homework Help in the USA

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Subjects Our System Dynamics Tutor Covers!

Our system dynamics tutor covers these topics:

Bifurcation Theory:

It addresses the issue of how parameter changes impact solution behavior. This subject has a solid algebraic/analytic bent. The learner will get knowledge of a variety of bifurcations. The Hopf bifurcation, in which a stable, steady-state solution transforms into an unstable periodic solution, is a crucial example.

Hamiltonian systems:

In these systems, at least one conserved quantity exists (energy). One type of similar transformation keeps a second quantity, such as area, volume, or a symplectic form. Such dynamical systems are standard and have unique characteristics.

Systems with mild initial conditions dependencies and chaotic systems:

This expands on a group of intriguing examples of hyperbolic dynamical systems that you can thoroughly examine using symbolic dynamics. Smale's Horseshoe is a significant classical example.

Ergodic theory:

Here, one learns about ergodic theorems (Birkhoff, Von Neumann), averages, invariant measures, and their significant generalization, the multiplicative ergodic theorem of Oscledec.

Theory of perturbation:

Since the sun is the most significant mass in planet motion, it alone essentially controls how each particular planet moves. The Keppler solutions, which result in elliptical planetary orbits, are comparable. In reality, other worlds with minor masses about the sun and possibly great distances from the planet of interest also affect how a single planet moves. As a result, it is possible to examine the variations in planetary velocity from a Keppler orbit in terms of power series that take into account the masses and distances of the other planets. It was at this point that perturbation theory was born. There are also significantly more advanced and contemporary techniques, such as the Kolmogorov-Arnold-Moser (KAM) theory.

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Recently Asked System Dynamics Questions

Expert help when you need it

Q1: Problem 2. (a) A tachometer has an analog display dial graduated in 5 rpm increments.The user manual states an accuracy of 1% of reading. Estimate the uncertainty in the reading at 10 rpm, 500 rpm and 5000 rpm. (b) A certain obstruction type flow meter (orifice, venturi, nozzle), shown in the following figure is used to measure the mass flow rate of air at low velocities. The relationship describing the flow rate is: \dot{m}=C A \sqrt{\left[\frac{2 g_{c} p_{1}}{R T_{1}}\left(p_{1}-p_{2}\right)\right]} where, * C = empirical-discharge coefficient. * A = flow area * T1 = upstream temperature * R = gas constant for air * Pi and p2 = upstream and downstream pressures, respectively. Calculate the percent uncertainty in the mass flow rate for the following conditions:See Answer
Q2: A non linear dynamic system is described by the following three state variable equations: \dot{q}_{1}=q_{2}-q_{3} \dot{q}_{2}=u+q_{2}+\frac{1}{2}\left|q_{1}\right| q_{1} \dot{q}_{3}=3 q_{1}+6 q_{3} Assume that \bar{q}_{3}=2 What is the value of \bar{q}_{1} ?See Answer
Q3: 1. Given the electrical circuit shown below (a) Obtain an equivalent rotational mechanical system free body diagram. (b) Obtain an equivalent translational mechanical system free body diagram. (c) Obtain the state variable form of the system in terms of electrical elements. See Answer
Q4: If the equations are linearized around the normal operating point, they can be put into matrix form as \dot{\hat{q}}=A \hat{q}+B \hat{u} where q=\left[q_{1} q_{2} q_{3}\right]^{T} What is the value of the A matrix? See Answer
Q5: 1. Consider the closed-loop system shown below: where K, > 0, K, > 0 and T > 0. Determine stability of the closed-loop system using Routh's stability criterion.See Answer
Q6: Problem 5. In the Problem 4, calculate the steady-state errors with the unit step (r(t) = 1)(5 points) and the unit ramp (r(t)3Dt) (5 points) references.See Answer
Q7: Problem 1. (a) A first order instrument is described by the following mathematical model: 2 \frac{d y}{d t}+30 y=120 The time constant of the system is 15 seconds. (b) The following spring-mass-damper system is: * Zero order * 1st Order * 2nd Order * 3rd Order * YES * NO (c) The natural frequency of the above system is: \omega_{\mathrm{n}}=\sqrt{\frac{M}{K}} * YES * NO (d) The damping ratio of the above system is: \zeta=\frac{f_{v}}{2 \sqrt{K M}} * YES *NO (e) A thermometer is an analog device (f) A pressure gauge is a digital device * YES * NO (g) The following signal has a frequency of 10-Hz. * YES * NO (h)A design stage uncertainty analysis is performed when there is a finite set of data available. * TRUE * FALSESee Answer
Q8: Below are three differential equations. From each one, find a (i) transfer function and (ii)the state space representation. The values that you'll use for the coefficients are different for each student and can be accessed in the accompanying excel document. For both the TF and SS, use f(t) as the input and x as the output. a_{1} \ddot{x}+b_{1} \ddot{x}+c_{1} \dot{x}+d_{1} x=f(t) b_{2} \ddot{x}+c_{2} \dot{x}+d_{2} x=f(t) c_{3} \dot{x}+d_{3} x=f(t) See Answer
Q9: a.Develop a model, i.e. differential equation(s), that describes the behavior of this system (10 points) b- What is one assumption you're making about the system? (5 points c. We are treating this as a linear time invariant system.What is a reason that the real system would not be linear? What is a reason that the real system would not be time invariant? (5 points)See Answer
Q10: What flow rate, win, is needed to maintain a steady state level of 0.2 m (7.5 points)? 1 Solve for how long it will take for the system to reach 63.2% of its steady state value (you do not have to solve the DE to find this!) (5 points) See Answer
Q11: 4. Give the differential equation to model the height h1 of the fluid system below. (Include cases where h1 > D and h1 < D.) See Answer
Q12: 5. For the following fluid system: Give a dynamic-systems model. Assume that h > h1 + h2 and h < h1 + h2 + h3. Assume that the length of the tank is 1 (for example, the area of the base is w1 · 1 = w1). b. Suppose that qmi = 3 kg / s. If h1 = h2 = h3 = 1 and w1 = 2, w2 = 4, w3 = 6, and R = 5. Assume p= 1 and g = 10 m/s. Find the steady-state value of h. Turn in all problem statements with your homework. Box all answersSee Answer
Q13: 3. Apply MATLAB to the previous problem in order to answer the following: а. Plot h1, h2 and h3 as a function of time when the input is the unit step function. Assume the initial conditions are h1 = 0, h2 = 10, and h2 = 5. Give all commands used to generate your plot. b. Plot the flows across each pipe as a function of time.See Answer
Q14: 2. For the fluid system below а.Give the dynamic systems model for h1, h2, and h3 in state variable matrix form. b. Determine the height of the water in each tank in steady state, assuming that A1 = 2, A2 = 3,A3 = 1, R1 = R2 = R3 = 1, qmi = 5 kg / s, g = 10 m² / s, p = 0.1 kg / m³. See Answer
Q15: The thin disk below turns on a massless arm B by way of a smooth bearing that keeps the axes of D and B aligned. The arm is hinged to the shaft driven at a constant angular speed N by a motor. The system is set up so that the arm is horizontal when the disk contacts the ground as shown. Assuming the disk of mass m rolls without slipping, find the force reactions and the moment reactions exerted by the arm on the bearings at point C in terms of the given dimensions, the mass,the normal force acting on the disk, the friction forces acting on the disk and the angular speed N. See Answer
Q16: Recall, the Eulerian angles that we defined in class as shown below. The axes (i, j, k) are fixed in body frame B and the axes (Î, Ĵ, K)of B with respect to mathF is represented through the angles (ø, 0, v) using a sequence about intermediate z, intermediate y and intermediate z-axis again to obtain body-fixed frame B in the final configuration, from the inertial reference frame F. This is often referred to as 3-2-3 sequence are fixed in the inertial reference frame F. The orientation or z-y-z sequence. You are hired as an control and navigation engineer at a satellite manufacturing firm. The satellite is equipped with thrusters which can rotate it about all the possible axes in the intermediate body-fixed frame at any given instant instead of just the y and z-axes. Now, there is a requirement to use a 2-1-3 sequence or the y-x-z sequence of successive rotations about the intermediate axes, \boldsymbol{F} \stackrel{\hat{J} \text { or } \hat{n}_{12}, \phi}{\longrightarrow} \mathbf{F}_{1} \stackrel{\hat{n}_{11} \text { or } \hat{n}_{21}, \theta}{\longrightarrow} \mathbf{F}_{2} \stackrel{\hat{n}_{23} \text { or } \hat{j}, \psi}{\longrightarrow} \mathbf{B} 1. Write down the individual rotation matrices for each of the Eulerian angles, i.e. Tó, Tạ, Ty. 2. Write the simplest angular velocity vector wB/F in terms of Euler angles according to the2-1-3 rotation sequence. Remember, the simplest expression is always written using basis vectors of intermediate reference frames. 3. Express the angular velocity vector wB/F in the second intermediate reference frame, F2, i.e.in terms of (în21, Ñ22, îÑ23)See Answer
Q17: 3. Consider the system shown in Fig. 3, and derive an equation of motion for the block of mass m1 - that is, find an expression for the acceleration x. The expression should not contain any other variables but will include parameters such as the angles ß and ø, the radius of the cylinder R, and the cylinder's mass m2 (the moment of inertia of the cylinder, about its center, is 1/2 m2 R^2). There is negligible friction between block mi and the surface on which it slides, but sufficient friction between the cylinder and its slope so that it rolls without slipping. The rope connecting the block to the cylinder has negligible mass and does not change length. The pulley over which the rope rides has negligible friction and negligible inertia. See Answer
Q18: Problem 3. In the Problem 2, find the range of K such that the closed-loop system is stable using Routh's stability criterion if it exists.See Answer
Q19: 3. Given is the system in the figure below. Determine a transfer function relating the output C(s) to the input R(s). Then, determine the value of k, such that the damping ratio 5=0.5. Calculate also the rise time tr, the peak time tp, the maximum overshoot M, and the settling time t, for a unit-step response. Find an analytical expression of c(t) for a unit-step input, given the calculated value of k, and plot the diagram. Finally, study the effect of k on the response of the system to a unit-step input via a parametric analysis: make ented MATLAB®scripts and the image of the plotted data. What is the value of k such that the system is critically damped? See Answer
Q20: 1. The following is a model of two rivers flowing into a lake. а.Give differential equations to model the fluid heights in each container. b. Write the state-variable equations in matrix form (there should be 3 variables). See Answer

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