7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with initial conditions x(0) = 0 and x'(0) = 0 Use the Laplace transform to determine the displacement of this system as a function of time in terms of a and b

7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with initial conditions x(0) = 0 and x'(0) = 0 Use the Laplace transform to determine the displacement of this system as a function of time in terms of a and b

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2

Q: • Suppose that the mass in a mass-spring-dashpot system with m = 25, c = 10, and k = 226 is set in…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: we considered the Position Servo described by the state equation where A = T x(t) = Ax(t) bu(t) + IT…

Q: A damping system with a negligibly small spring constant is modelled by x"+bx'=aebt with x(0)=0 and…

Q: Determine the constants a, p, yo and y'o so that Y(s) = Bs + C (s + D)² is the Laplace transform of…

Q: 3). y" + 2y' - 8y = 24, Given the IVP: y(0) = 0, y'(0) = -6. A) Use the Laplace transform to find…

Q: 6. A mass-spring-damper system has the equation ma" + ßx' + kx = F(t), where r(t) is th displacement…

A: Given , mass-spring-damper system equation as- mx''+βx'+kx=Ft To find the units of β and k in the…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Solution

Q: Use laplace transform to solve the initial value problem; a) y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

A: We have to find Laplace transform of y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

Q: The motion of a mass-spring system with damping is governed by y''(t) + by' (t) + 9y(t) = 0; y(0) =…

A: Given differential equationy″+by′+9y=0Let y=ert be the trial solution thenr2ert+brert+9ert=0Since…

Q: A mass weighing 6 Ib stretches a spring 3.5 inches. The mass is given a positive displacement of 5…

A: The weight w will be 6 lb and the length of the spring (L) is 3.5 inch which will be 3.512ft. The…

Q: A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then…

Q: solve for Y(s), the Laplace transform of the solution y(t): y'' +6y'+5y=te^t where y(0)=2 and…

Q: A 1-kilogram mass is attached to a spring whose constant is 14 N/m, and the entire system is then…

A: for spring mass problems there equations for the different situations are given as follows no…

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A: Draw the figure, which is given below. In equilibrium, mg−kx0=0⇒mg=kx0 Given, mg=4 and x0=1…

Q: A mass weighing 5 lb stretches a spring 3.5 inches. The mass is given a positive displacement of 9…

A: The weight w will be 5 lb. and the length of the spring (L) is 3.5 inch which will be 3.512ft. The…

Q: Please help me find the laplace transform of the following equation: 0.00174y''+0.295y'+25y=200u(t)…

A: If Ys is Laplace transform of yt. Then Laplace transform of y' and y'' when y(0)=0, y'(0)=0 is sYs…

Q: 1.Solve the following polynomial equations. a) 2X3+1=x2+2X

Q: The Federation starship Enterprise is running out of fuel and therefore has an exponentially…

A: Here's a step-by-step calculation of each problem: (a): Find v(t) and sketch a graph of v(t)Given…

Q: - y"+2y'-3y= 32e*; y'(0) =12, y(0) = 0 dy +2y 0; y=1 at t=0, y(0) = 1 dt dy +2y = cost; y(0) = 0 dt…

Q: 2. A particle starting with velocity u is falling freely under gravity with a constant acceleration.…

A: Introduction :

Q: Solve the initial value problem using Laplace transform b) y" + 3y' + 2y = 2 8(t-3), y(0)=0,…

A: Laplace and inverse Laplace transform

Q: 1. A spring with a mass of 2 kg requires a force of 6N to stretch the spring 0.5m beyond its natural…

Q: Consider a driven oscialting spring-mass system modeled by my'' + by' + ky = Fo cos(wt). Find the…

A: As given in the question

Q: у" - 5у' + бу %3D7 УО) %3 2, у' (0) — 4

A: We use the following standard results to solve the given problem.…

Q: Consider a driven oscialting spring-mass system modeled by my'' + by' + ky = Fo cos(wt). Find the…

A: Given: m=5kg K=10 N/M C=5Nsm Natural frequency ωn=km=105=2=1.4142 Critical damping coefficient…

Q: Q1) Solve the Second Order Deferential Equation by using Laplace Transform. y" + 6y' + 8y = 0, y(0)…

Q: 3. (Free-driving force, damped mass-spring system). Recall that the underdamped motion of the system…

Q: If r(t) = cos(5t)i+ sin(5t)j + Otk compute r'(t)= i+ j+ k and ſr(t) dt= i+ j+ k +C with C a constant…

A: Given, rt=cos5ti+sin5tj+0t k Find the value of r't and ∫r'tdt.

Question

100%

7. A damping system with a negligibly small spring constant is modelled by
x' + bx' = a eb1
with
initial conditions x(0) = 0 and x'(0) = 0
Use the Laplace transform to determine the displacement of this system as a function of time in terms
of a and b

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Page 1

Page 2

Page 3

Page 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Laplace Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Laplace under initial conditions x '+ y' + x= 0 and x '+ 2y' = 1 equation system x(0) = y (0) = 0Solve using the transform.
Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less than or equal to 5 and x is greater than or equal to -5 and less than or equal to 5). Sketch the solution curves with initial values y(0) = 2 y(0) = -2 y(-4) = 3 y(-4) = -3
The two-dimensional Laplace equation, f(x,y) = 5x-9y-6 2²4 2²4 -= 0, describes potentials and steady-state temperature distributions in a plane. Show that the following function satisfies the two-dimensional Laplace equation. dx
dy/dt = (y+1/2)(y+t) Use a slope field to explain why the solution that passes through (0,1) is never crossing the line y = 0.
Solve for the general solution of the equation: 2x’’+ 200x = 0. Show all math steps.
3) The vertical displacement from its natural length of a spring mass system is described by y"LE) + Ty'Lt) + 12 ylt) = 3, where timet is measured in seconds, using laplace transform solve the DE of the position of the mass after t = 20 seconds if the initial position is y(t) = 0 m/s and initial velocity y'lt) = -1 m/s when E=0.
y''- 9y = f(t) ...
Use laplace transform to find the initial value problem; a) y''+2y=alpha(t-1),y(0)=0,y'(0)=1
A radioactive material went through a decaying process as given in the following function f (t): f(t) = 5e-at where a is a constant attribute of the radioactive material and t is the time unit.
2) Assume that the motion of a mass-spring system with damping is governed by d+b+8y = 0, y(0) = 1, y'(0) = 0. Find the equation of motion for b = 3.
Assume the motion of a mass-spring system with damping is governed by d²x dx 1 +b +16x=0; x(0) - —, x(0)-0. di? ,2 dt Find the equation of motion and sketch the graph for the three cases where b= 4, 8, and 1
Laplace solves the Initial Value ProblemFind by transform.