Answered: Response of First-Order Systems and… | bartleby

Related questions

Question

Response of First-Order Systems and Time Constant Problem:

Find the free-vibration response and the time constant, where applicable, of systems governed by the following equations of motion:

(Note: The time constant can also be defined as the value of time at which the step response of a system rises to 63.2% (100.0% — 36.8%) of its final value.)

a. 100i + 20v = 0, v(0) = v(t = 0) = 10
b. 100i + 20v = 10, v(0) = v(t = 0) = 10
c. 100i – 20v = 0, v(0) = v(t = 0) = 10
d. 500à + 50w
%3D
%3D
0, w(0) = w(t = 0) = 0.5
%3D
%3D

Expert Solution

Step by step

Solved in 4 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Find the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.
A 330-kg wooden raft floats on a lake. When a 70-kg man stands on the raft, it sinks 3.9 cm deeper into the water. When he steps ff, the raft oscillates for a while. Part A What is the frequency of oscillation? Express your answer using two significant figures. Η ΑΣφ Hz Submit Request Answer Part B What is the total energy of oscillation (ignoring damping)?
Please write the units
A small piece of rounded stone perforated for threading is sliding on a wire which is hanging freely in the shape of a cosh function. Assume the stone moves with no friction. For very small displacements in x, what is the frequency of oscillation? You may use for the height of the wire and thus the height of the stone as a function of x the Taylor series expansion of cosh. G(x) =1 + x2/2 + x4/24 + ...
The motion of a rail car is recorded and found to have an overall grms level of 0.23 Grms. This data is used to reproduce the motion in the lab on a random vibration table. What grms level would the PSD profile need to be scaled to for simulation of a 10 hour train ride in 3 hours in the lab?
Do not copy
Item 1 Learning Goal: To understand the application of the general harmonic equation to the kinematics of a spring oscillator. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x = 0. The length of the relaxed spring is L. (Figure 1) The block is slowly pulled from its equilibrium position to some position init> 0 along the x axis. At time t = 0, the block is released with zero initial velocity. The goal is to determine the position of the block (t) as a function of time in terms of w and init It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C and S in terms of w and init Figure 1 of 3 L Xinit win x = 0 Part A Using the…
Problem 2 (Estimating the Damping Constant). Recall that we can experimentally mea- sure a spring constant using Hooke's law-we measure the force F required to stretch the spring by a certain y from its natural length, and then we solve the equation F = ky for the spring constant k. Presumably we would have to determine the damping coefficient of a dashpot empirically as well, but how would we do so? As a warm-up, suppose we have a underdamped, unforced spring-mass system with mass 0.8 kg, spring constant 18 N/m, and damping coefficient 5 kg/s. We pull the mass 0.3 m from its rest position and let it go while imparting an initial velocity of 0.7 m/s. %3D (a) Set up and solve the initial value problem for this spring-mass system. (b) Write your answer from part (a) in phase-amplitude form, i.e. as y(t) = Aeºt sin(ßt – 4) and graph the result. Compare with a graph of your answer from (a) to check that you have the correct amplitude and phase shift. (c) Find the values of t at which y(t)…
Help me with this question, please, only typing
A block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 2.44 Hz. The coefficient of static friction between block and surface is 0.373. How great can the amplitude of the SHM be if the block is not to slip along the surface? Number i Units
PRACTICE IT Use the worked example above to help you solve this problem. A 0.545 kg object connected to a light spring with a spring constant of 19.0 N/m oscillates on a frictionless horizontal surface. (a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm. E = J m/s V max = (b) What is the velocity of the object when the displacement is 2.00 cm? ± m/s (c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm. KE = J J PES= EXERCISE For what values of x is the speed of the object 0.14 m/s? x = ± cm HINTS: GETTING STARTED I I'M STUCK!
There is a block that is moving along on a wooden plank that moves and follows simple harmonic motion with a frequency of 15 oscillations per minute. In one oscillation, the motion of the center of mass of the object spans 3 m along the x-axis. Please determine the minimum value of the static friction coefficient that stops the block from slipping? Please determine the position, velocity and acceleration of the block 0.5 second after going through the center of the trajectory in the negative x-direction?