Question

Determine the transfer function.Please Help me!

Screenshot_20210421-103131.pngScreenshot_20210421-103913.png

The system shown in Figure simulates a machine supported by rubbers, which are approximated as four identical spring-damper units. The input is the force \(f\) and the output is the displacement \(x\) of the mass. The parameter values are \(m=500 \mathrm{~kg}, b=250 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\), and \(k=200,000 \mathrm{~N} / \mathrm{m}\)

a. Draw the necessary free-body diagram and derive the differential equation of motion.

b. Determine the transfer function. Assume zero initial conditions.

c. Determine the state-space representation.

d. Find the transfer function from the state-space form and compare with the result obtained in Part (b).

2 0

> Interesting ask!

Samuelmiros Thu, Apr 22, 2021 10:17 PM

Add a comment Improve this question Transcribed image text
Answer #1

-Solution - @ Free body diagram (FBD) Applying 20. Erama ( +) 400m F-4000-4000 - 125-1256 = 90st 12s 20 i +8250% +800 x = X-1Taking Laplace SX = X2 » Xg=SX 2022 = -250 x 800x, tf Taking lablace 205 X2 = -280 X2-800x + F 3205² X = -250 sx - 800x, +F [

> Thanks so mucho!

Melissa Pineda Thu, Apr 22, 2021 11:09 PM

> OMG quick answer

Kelly Alda Thu, Apr 22, 2021 11:15 PM

Add a comment
Know the answer?
Add Answer to:
Determine the transfer function.Please Help me!
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and it...

    Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...

  • Determine the transfer function of the system ***with an added inductor***. Then determine the state space...

    Determine the transfer function of the system ***with an added inductor***. Then determine the state space representation of the system shown with an added inductor. us Question Determine the Transfer Function of the systern in Problem #2, but now added into the circuit (figure below). (4 points) a) ith an inductor b) Determine the State-Space representation for the system with R. b6m

  • Need Matlab for part d) 3. The following questions relate the figure below of 2 couple...

    Need Matlab for part d) 3. The following questions relate the figure below of 2 couple spring-mass systems T2 fint) (a) Derive the 2 differential equations (one for each mass) of this system (b) Now derive the Transfer-Function from fin → Xi (c) Now derive the state-space representation (A,B,C,D) of this system. Hint: There should be 4 states (position and velocity of each mass). The output of this system is still y (which will probably be the first state in...

  • Application 1. Apply the state-space theory to determine a representation for the system.

    (Course Objective 2.1, Outcome m) Application 1. Apply the state-space theory to determine a representation for the system. Differential Eq.1Differential Eq.2 Laplace Transform Transfer Function 

  • Consider a mass-spring-damper system (i.e., the plant) described by the following second-order differential equation wh...

    Consider a mass-spring-damper system (i.e., the plant) described by the following second-order differential equation where y represents the position displacement of the mass. Our goal is to design a controller so that y can track a reference position r. The tracking error signal is then et)(t). (a) Let there be a PID controller Derive the closed-loop system equation in forms of ODE (b) Draw the block diagram of the whole system using transfer function for the blocks of plant and...

  • June 18, 2019 2. A system is characterized by the following differential equation: (18 pts) y)...

    June 18, 2019 2. A system is characterized by the following differential equation: (18 pts) y) + 2¢(t) +4y(t) = ü(t) +6u(t). A. Determine the transfer function, Y(s)/U(s). B. Derive a state-space representation (using matrices) for the system WITHOUT using Equations (2-34), (2-35) and (2-36) in the required textbook since all these equations have not been presented in class. C. Draw the simulation diagram that corresponds to the state-space representation in Part B June 18, 2019 2. A system is...

  • Consider the differential equation y(t) + 69(r) + 5y( Q3. t)u(t), where y(0) (0)0 and iu(t) is a ...

    Matlab code for the following problems. Consider the differential equation y(t) + 69(r) + 5y( Q3. t)u(t), where y(0) (0)0 and iu(t) is a unit step. Deter- mine the solution y(t) analytically and verify by co-plotting the analytic solution and the step response obtained with the step function. Consider the mechanical system depicted in Figure 4. The input is given by f(t), and the output is y(t). Determine the transfer function from f(t) to y(t) and, using an m-file, plot...

  • Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is...

    Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and b is the viscous friction coefficient of the ball bearing that supports the right shaft and acts as a linear viscous damper with rotary motion. The left shaft is only supported by the right shaft, so there...

  • P4: The car model of a cruise control system is given in the following transfer function...

    P4: The car model of a cruise control system is given in the following transfer function block diagram ms + b Where v is the car speed u is the control force m is the mass of the vehicle, 1000 kg b is the damping coefficient, 50 N s/m More details are available here (1) Derive the differential equation relating y(t) to u(t) (2) Determine the time constant of the car dynamics (from u to v) If a proportional feedback...

  • A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1....

    A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT