Consider a dynamical system that consists of a cart with an inverted pendulum (pointmass on a massless shaft) attached to it as depicted in Figure 3.19.m = 0.1 kgDistance xl = 1 mg = 10 m/s²Massless shaftForce uM = 1 kgFrictionlessFigure 3.19 An inverted pendulummoving on a cart of Exercise 3.18.surface(a) Obtain a nonlinear state-space model of the system using the state variablesX1 = x,X2 = i,X3 = 0,X4 = 0.Designate x1 as the system output.

Given data: The state variables: x1=x x2=x. x3=θ x4=θ. Mass, M=1 kg Mass, m=0.1 kg

Answered: Consider a dynamical system that…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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97 K/s ll O &e 7:23 ۱۰۳۹ من ۱۰۶۰ PROBLEMS 77 will jump outward. We expect the bifurcation point, the point where the equation significance. As we shall see in Example 3.10, w= Vg/l is the oscilla- tion frequency, in radians per second, of a simple pendulum of length I. If the rotation frequency is less than this value, the pendulum can hang vertically. (It could also swing back and forth, executing pendulum mo- tion.) However, for a rotation frequency higher than the pendulum fre- quency, the pendulum will fly outward, unless it is precisely vertical. Can you see why this is so? motion suddenly has two solutions, has some special The moral of this example is that it is important to check that a mathe- matical solution makes good physical sense. Problems For problems marked *, refer so page 520 for a hint, clue, or answer. 2.1 Time-dependent force* A S-kg mass moves under the influence of a force F (4ri-3j)N, where t is the time in seconds (1 N = 1 newton). It starts at rest from the…
A 5 kg oscillator has a speed of 6.5 m/s when its displacement is 1.5 m and 2.9 m/s when its displacement is 9.7 m. What is the oscillator's maximum speed?
Please please answer super fast
A small block of mass M = 850 g is placed on top of a larger block of mass 3M which is placed on a level frictionless surface and is attached to a horizontal spring of spring constant k = 3.5 N/m. The coefficient of static friction between the blocks is μ = 0.2. The lower block is pulled until the attached spring is stretched a distance D = 1.5 cm and released.Randomized Variables M = 850 gD = 1.5 cmk = 3.5 N/m a) Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m/s2. b) Write an equation for the largest spring constant kmax for which the upper block does not slip. c) Calculate a value for the largest spring constant kmax for which the upper block does not slip, in N/m.
Kindly answer number 2 with complete solution
A stiff spring k = 666 N/m has be attached to the floor vertically. A mass of 6.66 kg is placed on top of the spring as shown below and it finds a new equilibrium point. If the block is pressed downward and released it oscillates. If the compression is too big, however, the block will lose contact with the spring at the maximum vertical extension. Draw a free body diagram and find that extension at which the block loses contact with the spring.
A car with a mass m = 1000.0kg is moving on a horizontal surface with a speed v = 20.0m/s when it strikes a horizontal coiled spring and is brought to rest when the spring is compressed by a distance d = 3.0m. Calculate the spring stiffness constant k by... (a) select appropriate common equations and make appropriate substitutions that are specific to the problem, and algebraically manipulate the equations to end with an algebraic expression for the variable the problem is asking you to solve for. (b) Show the numeric substitution of given quantities and show the final numeric result. (c) Draw a free body diagram for the system and define the given quantities.
Problem 11: A small block of mass M= 350 g is placed on top of a larger block of mass 3M which is placed on a level frictionless surface and is attached to a horizontal spring of spring constant k = 1.9 N/m. The coefficient of static friction between the blocks is μ =0.2. The lower block is pulled until the attached spring is stretched a distance D = 2.5 cm and released. Randomized Variables M = 350 g D = 2.5 cm k = 1.9 N/m Part (a) Assuming the blocks are stuck together, what is the maximum magnitude of acceleration amax of the blocks in terms of the variables in the problem statement? amax = k D/(3 M+M ) ✓ Correct! Part (b) Calculate a value for the magnitude of the maximum acceleration amax of the blocks in m/s². ✓ Correct! | @mar= 0.03390 Part (c) Write an equation for the largest spring constant kmax for which the upper block does not slip. Kmax = μ (M +M) g/kl
Part A: The position of a 40 gg oscillating mass is given by x(t)=(2.0cm)cos(10t)=(2.0cm)cos⁡(10t), where t is in seconds. Determine the velocity at t=0.40s=0.40s. Express your answer in meters per second to two significant figures. Part B: Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be? Express your answer in newtons per meter to two significant figures. Part C: What is the total energy E of the mass described in the previous parts? Express your answer in joules to two significant figures.
A 6 kg mass swings on a long 6.2 m-string as a pendulum. What is the period of the pendulum to the nearest 0.1 s?
Note: Because the argument of the trigonometric functions in this problem will be unitless, your calculator must be in radian mode if you use it to evaluate any trigonometric functions. You will likely need to switch your calculator back into degree mode after this problem.A massless spring is hanging vertically. With no load on the spring, it has a length of 0.24 m. When a mass of 0.59 kg is hung on it, the equilibrium length is 0.98 m. At t=0, the mass (which is at the equilibrium point) is given a velocity of 4.84 m/s downward. At t=0.32s, what is the acceleration of the mass? (Positive for upward acceleration, negative for downward)
A ball is dropped from a platform starting from rest. After 4s, another ball is thrown downwards from the same platform with a speed U. The two balls meet at t =18s. What is the value of the initial velocity of the second ball? A pendulum oscillates as shown in the figure. A and C are the highest points of oscillation and B is the lowest point. Identify the forms of energy the pendulum bob has, and how they are changed and transferred during the oscillation. Explain. A B.

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