Periodic Function Word Problems

A Ferris wheel has a diameter of 50 feet and makes one full rotation every 40 seconds. What is the amplitude, period, and midline of the function that models the height of a passenger over time?

• amplitude: 50, period: 40, midline: 25

• { "amplitude": 25, "period": 40, "midline": 0 }

• amplitude: 25, period: 20, midline: 10

• amplitude: 50, period: 20, midline: 0

A pendulum on a grandfather clock swings back and forth, reaching a maximum height of 1.5 meters and a minimum height of 0.5 meters. If it takes 2 seconds to complete one full swing, what is the amplitude, period, and midline of the function that models the height of the pendulum over time?

• amplitude: 0.5, period: 1, midline: 0.5

• amplitude: 1.5, period: 1, midline: 0.5

• { "amplitude": 0.5, "period": 2, "midline": 1 }

• amplitude: 1, period: 2, midline: 0.75

The temperature in a room oscillates between 68°F and 72°F over a 24-hour period. What is the amplitude, period, and midline of the function that models the temperature in the room over time?

• amplitude: 4, period: 12, midline: 70

• {'amplitude': 2, 'period': 24, 'midline': 70}

• amplitude: 24, period: 2, midline: 70

• amplitude: 2, period: 12, midline: 70

A sound wave has a maximum pressure of 2.5 atmospheres and a minimum pressure of 1.5 atmospheres. If it takes 0.02 seconds to complete one cycle, what is the amplitude, period, and midline of the function that models the pressure of the sound wave over time?

• midline: 3 atmospheres

• { "amplitude": "1 atmosphere", "period": "0.02 seconds", "midline": "2 atmospheres" }

• period: 0.2 seconds

• amplitude: 0.5 atmospheres

The water level in a harbor fluctuates between 3 meters and 5 meters over a 6-hour period. What is the amplitude, period, and midline of the function that models the water level in the harbor over time?

• amplitude: 3, period: 8, midline: 4.5

• {'amplitude': 1, 'period': 6, 'midline': 4}

• amplitude: 1.5, period: 5, midline: 4.2

• amplitude: 2, period: 4, midline: 3.5

A spring oscillates with a maximum displacement of 0.2 meters and a minimum displacement of -0.2 meters. If it takes 0.5 seconds to complete one full cycle, what is the amplitude, period, and midline of the function that models the displacement of the spring over time?

• {"amplitude": 0.2, "period": 0.5, "midline": 0}

• amplitude: 0.1, period: 0.3, midline: 0.5

• amplitude: 0.5, period: 0.2, midline: 0.2

• amplitude: 0.3, period: 0.7, midline: 0.1

The voltage in an electrical circuit varies between 10 volts and 14 volts over a 60 Hz cycle. What is the amplitude, period, and midline of the function that models the voltage in the circuit over time?

• {'amplitude': 2 volts, 'period': 1/60 seconds, 'midline': 12 volts}

• amplitude: 1 volt, period: 1/70 seconds, midline: 15 volts

• amplitude: 5 volts, period: 1/30 seconds, midline: 11 volts

• amplitude: 3 volts, period: 1/50 seconds, midline: 13 volts

A radio wave has a maximum amplitude of 100 millivolts and a minimum amplitude of 20 millivolts. If it takes 0.001 seconds to complete one cycle, what is the amplitude, period, and midline of the function that models the amplitude of the radio wave over time?

• amplitude: 120, period: 0.002, midline: 40

• { "amplitude": 80, "period": 0.001, "midline": 60 }

• amplitude: 60, period: 0.01, midline: 90

• amplitude: 40, period: 0.005, midline: 70

The height of a bouncing ball oscillates between 1 meter and 2 meters over a 2-second period. What is the amplitude, period, and midline of the function that models the height of the ball over time?

• {'amplitude': 0.5, 'period': 2, 'midline': 1.5}

• amplitude: 0.3, period: 4, midline: 1.8

• amplitude: 1, period: 3, midline: 2

• amplitude: 0.8, period: 1, midline: 1.2

The intensity of a light wave varies between 0.5 watts and 1.5 watts over a 0.01 second period. What is the amplitude, period, and midline of the function that models the intensity of the light wave over time?

• {'amplitude': 0.5, 'period': 0.01, 'midline': 1}

• amplitude: 0.8, period: 0.02, midline: 1.2

• amplitude: 0.75, period: 0.005, midline: 0.75

• amplitude: 1.5, period: 0.01, midline: 0.5