1. A standard pendulum of length L that swings under the influence of gravity alone (no...

 

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1. A standard pendulum of length L that swings under the influence of gravity alone (no air resistance) has a period (the time for one complete swing) in seconds of T=- du @JO V1-k² sin²(u) where w² = g/L, k² = sin²(0/2), g = 9.8 m/s² is the free-fall acceleration, and 0, is the initial angle from which the pendulum was released, in radians, measured from the vertical. Use the trapezoidal rule to estimate the period of a 1 metre long pendulum that is released from an angle of 0,= π/4. Ensure that your estimate is correct with an error of less than 0.01 seconds. You will need to first determine how many trapezoids are needed to obtain this error bound. 1. A standard pendulum of length L that swings under the influence of gravity alone (no air resistance) has a period (the time for one complete swing) in seconds of T=- du @JO V1-k² sin²(u) where w² = g/L, k² = sin²(0/2), g = 9.8 m/s² is the free-fall acceleration, and 0, is the initial angle from which the pendulum was released, in radians, measured from the vertical. Use the trapezoidal rule to estimate the period of a 1 metre long pendulum that is released from an angle of 0,= π/4. Ensure that your estimate is correct with an error of less than 0.01 seconds. You will need to first determine how many trapezoids are needed to obtain this error bound.

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