2nd order differential equation problem with sin(theta)

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SUMMARY

The discussion centers on solving the second-order differential equation θ''(t) = c*sin[θ(t)], which models the behavior of a catapult over time. The user attempted to use Maple for a solution but encountered a complex integral involving a Jacobian amplitude. They considered a small angle approximation but noted that the angle θ is constrained between 0 and π/2. The transformation of the equation into a separable form using the chain rule is highlighted as a key step in the solution process.

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  • Understanding of second-order differential equations
  • Familiarity with the chain rule in calculus
  • Experience with Maple software for mathematical computations
  • Knowledge of Jacobian amplitudes and their applications
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Mathematicians, physicists, and engineers involved in modeling dynamic systems, particularly those interested in differential equations and their applications in real-world scenarios like catapults or pendulums.

Robin64
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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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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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