How do you solve a nonhomogeneous second order ODE with a cosine function?

  • Thread starter Stu165
  • Start date
  • Tags
    Ode
In summary, the conversation is about solving a physics problem involving an equation with the variables m, wsubo, and F. The solution is given as x(t) = xsubo cos wt and the goal is to show that this is a valid solution. After some discussion and calculations, it is determined that x(t) = xsubo cos wt is indeed a solution to the equation. The conversation also mentions working with undetermined coefficients and the double-posting of the question.
  • #1
Stu165
10
0
Can anyone give me a hand with this, cause I'm stumped and can't remember exactly how to go about solving this.

here's the eqn

m[d^2x/dt^2 + wsubo^2 x] = F cos wt

I'm supposed to show that x(t) = xsubo cos wt

w is the incident freq
wsubo is the resonant freq
m is mass

it's from physics but the principles are just maths.
 
Physics news on Phys.org
  • #2
Since you are given the solution, just plug it into the eqn. I get a solution only when [tex]x_0=\frac{w^2-F}{w^2}[/tex].
 
Last edited:
  • #3
I would have thought you would have to work with undetermined coefficients or something
 
  • #5
Stu165 said:
I would have thought you would have to work with undetermined coefficients or something

No, you were not asked to SOLVE the equation, only to show that
x(t) = x0 cos wt IS a solution.
 
  • #6
I just found this out, by plugging in xsubocoswt, I got F = m (wsub0^2 - w^2) x

by then using undetermined coefficients I get a value of

y(t) = F / m (wsub0^2 - w^2) coswt

by substituting F in I get the xcos wt
 

Related to How do you solve a nonhomogeneous second order ODE with a cosine function?

1. What is a second order nonhomogeneous differential equation?

A second order nonhomogeneous differential equation is a mathematical equation that includes a second derivative of a function, as well as a non-zero function on the right side of the equation. It is used to model physical phenomena that involve acceleration or other related quantities.

2. How do you solve a second order nonhomogeneous differential equation?

To solve a second order nonhomogeneous differential equation, you can use the method of undetermined coefficients or the method of variation of parameters. Both methods involve finding a particular solution and adding it to the general solution of the corresponding homogeneous equation.

3. What is the difference between a homogeneous and nonhomogeneous differential equation?

A homogeneous differential equation has a zero function on the right side of the equation, while a nonhomogeneous differential equation has a non-zero function on the right side. The solutions to a homogeneous equation form a vector space, while the solutions to a nonhomogeneous equation do not.

4. What are initial conditions in a second order nonhomogeneous differential equation?

Initial conditions in a second order nonhomogeneous differential equation are the values of the dependent variable and its first derivative at a specific point. These conditions are used to find the particular solution to the equation.

5. Can you use Laplace transforms to solve a second order nonhomogeneous differential equation?

Yes, you can use Laplace transforms to solve a second order nonhomogeneous differential equation. This method involves transforming the equation into an algebraic equation, solving for the unknown function, and then using the inverse Laplace transform to find the solution.

Similar threads

I Question about solving linear first order non-homogeneous ODEs
    • Differential Equations
Replies
3
Views
851
I Solving an ODE with Legendre Polynomials
    • Differential Equations
Replies
1
Views
2K
I Solve second order linear differential equation
    • Differential Equations
Replies
7
Views
1K
How to Approach Solving a Nonlinear Second Order ODE with a Quadratic Term?
    • Calculus and Beyond Homework Help
Replies
4
Views
565
I Can you check the solution for this second order ODE?
    • Differential Equations
Replies
6
Views
2K
MHB Solving 1st order non-linear ODE
    • Differential Equations
Replies
4
Views
2K
I Constructing a 2nd order homogenous DE given fundamental solution
    • Differential Equations
Replies
3
Views
1K
I Using complex numbers or phasor transform to solve O.D.E's
    • Differential Equations
Replies
3
Views
2K
I Second order DE with Sine function
    • Differential Equations
Replies
6
Views
1K
I How to find the integrating factor? (1st order ODE)
    • Differential Equations
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top