The angular displacement 6 (in radians) of a pendulum swinging through a small angle with limited air resistance and Internal friction can be approximated by the simple harmonic motion models θ=asinωt or θ=acosωt . The period T (time required for one back-and-forth swing) Is given by T=2π√Lg , where L is the length of the pendulum and g is the acceleration due to gravity. The maximum angular displacement is al and positive angles are taken to the right of the center position. Use this information for Exercises 33-34.
33. A 4-ft pendulum is initially at its right-most position of 12°.
a. Determine the period for one back-and-forth swing. Use g = 32 ft/sec2.
b. Write a model for the angular displacement
θ of the pendulum after t seconds, (Hint: Be sure to convert the initial position to radians.)
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