# 2nd order differential equation problem with sin(theta)

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• Robin64
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.
Robin64
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?

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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## 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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