Differentiating to obtain dtf/dt gives:

de dt"

dx dt dx dt

Differentiating to obtain d'"0/dt~ gives:

tlxV

d20 <U2

Substituting the expressions for dWdt* and sin 9 in the differential equation gives:

d2x dt2

Unfortunately, the solution to this equation can not be expressed in finite form in terms of elementary functions of t. The situation encountered here is similar to that which arises in the mechanics of a simple pendulum. In the case of the simple pen-

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