An alternating curent generator in the United Kingdom generates current with a frequency of 50 Hz. Suppose that initially, the current is at its maximum of 12 amperes. If the current varies in simple harmonic motion over time, write a model for the current I (in amperes) as a function of the time t (in seconds).

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32. An alternating current generator in the United Kingdom generates current with a frequency of 50 Hz.
Suppose that initially, the current is at its maximum of 12 amperes. If the current varies in simple
harmonic motion over time, write a model for the current I (in amperes) as a function of the time t (in
seconds).
The angular displacement 0 (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 0 = a sin ot
or 8 = a cos ot. The period T (time required for one back-and-forth swing) is given byT- 27
where L is the length of the pendulum and g is the acceleration due to gravity. The maximum angular
displacement is |a| and positive angles are taken to the right of the center position. Use this information
for Exercises 33-34.
Transcribed Image Text:32. An alternating current generator in the United Kingdom generates current with a frequency of 50 Hz. Suppose that initially, the current is at its maximum of 12 amperes. If the current varies in simple harmonic motion over time, write a model for the current I (in amperes) as a function of the time t (in seconds). The angular displacement 0 (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 0 = a sin ot or 8 = a cos ot. The period T (time required for one back-and-forth swing) is given byT- 27 where L is the length of the pendulum and g is the acceleration due to gravity. The maximum angular displacement is |a| and positive angles are taken to the right of the center position. Use this information for Exercises 33-34.
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