Differential equation with laplace transform and springs

In summary, the conversation discusses the given amplitude and a value for the frequency of a periodic function and how to obtain the Laplace transform of such a function. The article provided explains the process of obtaining the transform in more detail.
  • #1
Sneakatone
318
0

Homework Statement


I do not know how to find f(t) with the given Ampliture 40 and a=pi
Untitled.png

Homework Equations

The Attempt at a Solution


I have the solution above.

my set up was 1/2y''+y'+5=f(t)

1/2S^2* Y(s) + Y(s)+5=f(t)
 
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  • #2
Have you studied periodic functions? Do you know how to obtain the Laplace transform of a periodic function?

Here is a brief article discussing how:

http://academic.udayton.edu/LynneYengulalp/Solutions219/LaplacePeriodicSolutions.pdf
 
Last edited by a moderator:
  • #3
Sneakatone said:

Homework Statement


I do not know how to find f(t) with the given Ampliture 40 and a=pi
View attachment 76100

Homework Equations

The Attempt at a Solution


I have the solution above.

my set up was 1/2y''+y'+5=f(t)

1/2S^2* Y(s) + Y(s)+5=f(t)

You want the LaPlace transform of f(t) on the right of that last equation. To see how to get the transform of a periodic function, look here:
http://www.intmath.com/laplace-transformation/5-transform-periodic-function.php
 
  • #4
SteamKing said:
Have you studied periodic functions? Do you know how to obtain the Laplace transform of a periodic function?

Here is a brief article discussing how:

http://academic.udayton.edu/LynneYengulalp/Solutions219/LaplacePeriodicSolutions.pdf

From the looks of this does amplitude not matter , only the period?
 
Last edited by a moderator:
  • #5
Sneakatone said:
From the looks of this does amplitude not matter , only the period?
Wrong. There is an ##f(t)## in the formula for the transform, so everything about ##f(t)## matters.
 

1. What is a differential equation with Laplace transform and how is it used in relation to springs?

A differential equation with Laplace transform is a mathematical tool used to model the behavior of a system, such as a spring, over time. The Laplace transform converts the differential equation into an algebraic equation, making it easier to solve and analyze the system's response.

2. How are springs represented in a differential equation with Laplace transform?

In a differential equation with Laplace transform, springs are represented as a second-order linear differential equation. This takes into account the spring's displacement, velocity, and acceleration, and how they change over time.

3. Can the Laplace transform be used to solve any differential equation related to springs?

Yes, the Laplace transform can be used to solve any linear differential equation related to springs. However, for more complex or nonlinear systems, other techniques may be necessary.

4. How does the Laplace transform make it easier to analyze springs?

The Laplace transform allows us to analyze the behavior of springs in the frequency domain, rather than the time domain. This makes it easier to understand the system's response to different frequencies of input and to determine its stability and resonance.

5. Are there any limitations to using a differential equation with Laplace transform for springs?

One limitation is that the Laplace transform assumes that the system is linear, which may not always be the case for springs. It also requires initial conditions and assumes that the system is in equilibrium. Additionally, the Laplace transform may not provide a physical understanding of the system's behavior, as it is a purely mathematical tool.

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