Consider the pendulum equations dx dt = y, dy dt = ?6 si
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Consider the pendulum equations dx dt = y, dy dt = ?6 sin x. If the pendulum is set in motion from its downward equilibr
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Consider the pendulum equations dx dt = y, dy dt = ?6 sin x. If the pendulum is set in motion from its downward equilibrium position with angular velocity ?, then the initial conditions are x(0) = 0, y(0) = ?. (a) Plot x versus t for ? = 3 and also for ? = 6. Explain the differing motions of the pendulum that these two graphs represent. (b) There is a critical value of ?, which we denote by ?c, such that one type of motion occurs for ? < ?c and a qualitatively different type of motion occurs for ? > ?c. Determine the value of ?c to two decimal places
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