2nd order differential equation problem with sin(theta)

In summary, the conversation discusses a differential equation involving θ''(t)=c*sin[θ(t)] and the difficulties in finding a solution. The speaker mentions trying to use Maple but getting a complex integral, and considering a small angle approximation. They clarify that the equation is not for a pendulum, but for modeling the behavior of a catapult. Suggestions are requested for solving the equation.
  • #1
Robin64
34
3
I have a differential equation that is essentially this: θ''(t)=c*sin[θ(t)] . I've been stymied trying to find a solution, and even when I tried using Maple, I got a nasty integral of a Jacobian amplitude. I'm tempted to use a small angle approximation, but the angle is 0≤θ≤π/2. I know this is similar to a pendulum, but it is not a pendulum (I'm modeling the the behavior of a catapult as a function of time). Any suggestions?
 
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  • #2
θ''(t)=dθ'/dt=c sinθ, use the chain rule to change the variables dθ'/dt=(dθ'/dθ)*(dθ/dt)=(dθ'/dθ)*θ' now sub. to the differential equation => θ'(dθ'/dθ)=c sinθ now it has been converted to separable differential equation.
<Mod note: Post edited to remove full solution>
 
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Related to 2nd order differential equation problem with sin(theta)

1. What is a 2nd order differential equation?

A 2nd order differential equation is an equation that involves a function and its first and second derivatives. It is used to model many physical phenomena in science and engineering.

2. What is the role of sin(theta) in a 2nd order differential equation?

Sin(theta) can represent a specific variable or function in a 2nd order differential equation, and it can also be used to solve the equation through various mathematical techniques.

3. How is a 2nd order differential equation with sin(theta) solved?

The specific method for solving a 2nd order differential equation with sin(theta) will depend on the specific equation and its initial conditions. However, it often involves using trigonometric identities and integration techniques.

4. What are some real-life applications of 2nd order differential equations with sin(theta)?

2nd order differential equations with sin(theta) can be used to model a variety of physical phenomena such as mechanical vibrations, electrical circuits, and fluid dynamics. They are also commonly used in engineering and physics research.

5. Are there any limitations to using 2nd order differential equations with sin(theta) in modeling real-life situations?

While 2nd order differential equations with sin(theta) can accurately model many physical phenomena, they may not be able to fully capture all aspects of a complex real-life situation. Additionally, they may require simplifying assumptions that may not hold true in certain scenarios.

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