Consider the system shown in Figure P 1.5 where a mass M is pulled by a driving force f(t) and is restrained by a linear spring K and an ideal dashpot B. Write the differential equation for the system in terms of the displacement variable x and determine the relative values of B and K to provide critical damping when f(t) is a unit step function. K IB M -f (t)

Consider the system shown in Figure P 1.5 where a mass M is pulled by a driving force f(t) and is restrained by a linear spring K and an ideal dashpot B. Write the differential equation for the system in terms of the displacement variable x and determine the relative values of B and K to provide critical damping when f(t) is a unit step function. K IB M -f (t)

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

See similar textbooks

Similar questions

The diagram shows a simple electric circuit consisting of a power source, a resistor, and an inductor. A model of the current I, in amperes (A), at time t is given by the first-order differential equation as attached. where E(t) is the voltage (V) produced by the power source, R is the resistance, in ohms (Ω), and L is the inductance, in henrys (H). Suppose the electric circuit consists of a 24-V power source, a 12-Ω resistor, and a 4-H inductor. (a) Sketch a slope field for the differential equation. (b) What is the limiting value of the current? Explain
The translational mechanical system shown in Figure Q1 is at rest for t < 0. The force u(t) is the input to the system and the displacements x1(t) and x2(t), are measured from their respective equilibrium positions. Ifm1 is1kg,k1 =k2 =k3 is1N/mandb1 =b2=b3=is1N-s/m,determine the transfer function for the system (?(?) = ?1(?)) ?(?)
A mass weighing 32 pounds stretches a spring 8 feet.(a) Define the differential equation that represents the above undamped mass-spring system.(b) Determine the amplitude and period of motion if the mass is initially released from apoint 1 foot above the equilibrium position with an upward velocity of 2 ft/s.(c) Now assume that the mass is attached to a dashpot device that offers a damping forcenumerically equal to 4 times the instantaneous velocity. Determine the motion (i.e., the solution)of the damped mass-spring system with the same conditions stated in (b).
For the system shown in figure (1) with unit step input. (1) Determine the value of N when the damping ratio (=0.6)? (2) Obtain rise time, peak time, and settling time for 5% of steady state error?
For the system given below, a) Find K1 and K2 so that the steady-state error is zero, the settling time is one second, and the overshoot is 5% for a unit step input. b) Specify the system type and find the steady-state error a unit ramp input using the computed K1 and K2 values. "Can you explain step by step " check image "
7.Differential equation for a simple wheelchair with a suspension system (bumper) can be written as: ?2???2+??????+????=1???. Fe is the gravitational force exerted by the sitting person, 800 N; “m” is mass of the wheelchair, 25 kg; “Ks” is the stiffness (inverse of compliance) of the spring, 2500 N/m; the damping coefficient of the dashpot “B” is 500N/(m/s). How much is the damping coefficient ?of the system? The original of the problem is attached.
a. The switch S1 is in the A position. Find the maximum IL1 that will flow. b. Find the steady state voltage across R1 when in S1 is in the A position for a very long time. c. The switch is moved to position B. Find the steady state current IL after a very long time. d. Using the information from part a,b,c find the equations that describes iL during the transient state after the switch is in position B.
Fig. Q1(b) shows a rotational mechanical system with two masses with moment of inertia, J1 and J2. The T(t) is the applied torque to J1, while the θ1(t) and θ2(t) are the angular displacement of J1 and J2, respectively. Draw the free-body diagrams of mass with moment of inertia J1 and mass with moment of inertia J2, and then develop differential equations (with constant J1, J2, D1, D2, and K in the equations) that represent the mechanical system. Then using the given value of the constants in Figure Q1(b), derive the transfer function G(s) = θ2(s)/T(s) and the block diagram of the system.
Use the differential equation for electric circuits given by L (dI/ dt) + RI + E. In this equation, I is the current, R is the resistance, L is the inductance, and E is the electromotive force (voltage). Solve the differential equation for the current given a constant voltage E0.
Not sure why I've had so many problems with this, I'm looking for examples to review before my test.... I'll like it when I receive it, just get me some examples... (Take a generic heavily used maxwell's equation) I need the differential form of Maxwell's equations (rather than the integral form)... So I would like a step-by-step example process turning the integral form of Maxwell's equations (WITHOUT any magnetic monopole terms but WITH all the standard terms) into their differential form.This link provides an example: https://www.wikihow.com/Convert-Maxwell%27s-Equations-into-Differential-Form
A 600-kg machine is mounted on a rigid floor of a factory through a spring of stiffness 1,500,000 N/m and a dashpot with unknown damping coefficient. The machine produces a constant harmonic force of 500 N. When the machine operates at 100 rad/s, its steadystate displacement amplitude is observed to be 0.0001 m. (a) Determine the damping coefficient of the dashpot, and compute the phase angle between the force and displacement at 100 rad/s. (b) Compute the values of the system’s undamped natural frequency, critical damping coefficient and damping ratio (c) Determine the velocity and acceleration amplitudes of the machine at 100 rad/s. (d) Evaluate the percentage change of the steady-state displacement amplitude and phase of the machine if the frequency is now increased to 150 rad/s.
If a=1.1 for G=1s3+6as2+11a2s+6a3 in the closed loop system in the figure, which of the following is the largest K value at which the system can be stable?