# Solve: #d^2x//dt^2 + g sin theta t =0# if # theta=g//l# , and g and l are constants?

You want to know how to solve:

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# x = l^2/g \ sin theta t + At + B #

We have:

which we could type as:

It is possible to "separate the variables" and obtain:

Additionally, integrating provides us with:

And when we keep doing so, we obtain:

So that:

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The solution to the differential equation ( \frac{{d^2x}}{{dt^2}} + g \sin(\frac{g}{l} t) = 0 ), where ( \theta = \frac{g}{l} ) and ( g ) and ( l ) are constants, involves solving the second-order linear homogeneous ordinary differential equation. This equation doesn't have a general analytical solution in terms of elementary functions. However, it can be solved numerically or approximated under specific conditions or using numerical methods.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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