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Ch 14: Periodic Motion
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 14: Periodic MotionProblem 6
Chapter 14, Problem 6

The wings of the blue-throated hummingbird (Lampornis clemenciae), which inhabits Mexico and the southwestern United States, beat at a rate of up to 900 times per minute. Calculate (a) the period of vibration of this bird's wings, (b) the frequency of the wings' vibration, and (c) the angular frequency of the bird's wing beats.

Verified step by step guidance
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To find the period of vibration (T), use the formula T = 1/f, where f is the frequency. First, convert the wing beat rate from beats per minute to beats per second by dividing 900 beats/minute by 60 seconds/minute.
The frequency (f) is the number of wing beats per second. After converting the wing beat rate to beats per second, you have the frequency in Hz (Hertz).
Now, calculate the period (T) using the formula T = 1/f. This will give you the time in seconds for one complete cycle of wing beats.
To find the angular frequency (ω), use the formula ω = 2πf, where f is the frequency in Hz. This will give you the angular frequency in radians per second.
Ensure all units are consistent and check your calculations for accuracy. The period will be in seconds, the frequency in Hz, and the angular frequency in radians per second.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Period of Vibration

The period of vibration is the time it takes for one complete cycle of motion. It is the reciprocal of frequency and is measured in seconds. For the hummingbird's wings, the period can be calculated by taking the inverse of the frequency, which is the number of wing beats per second.
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Frequency

Frequency refers to the number of complete cycles or vibrations per unit of time, typically measured in hertz (Hz). In this context, it is the number of times the hummingbird's wings beat in one second. To find the frequency, divide the number of beats per minute by 60.
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Angular Frequency

Angular frequency is a measure of how quickly an object rotates or oscillates, expressed in radians per second. It is related to the frequency by the formula ω = 2πf, where ω is the angular frequency and f is the frequency. This concept helps describe the rotational aspect of the wing beats.
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Related Practice
Textbook Question

A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 shows a graph of the ball's position x as a function of time t. What are the oscillation's (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?

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Textbook Question

In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring's force constant.

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Textbook Question

The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (c) the period? (d) the angular frequency of this motion?

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Textbook Question

A 2.40-kg ball is attached to an unknown spring and allowed to oscillate. Figure E14.7 shows a graph of the ball's position x as a function of time t. What are the oscillation's (a) period, (b) frequency, (c) angular frequency, and (d) amplitude? (e) What is the force constant of the spring?

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A machine part is undergoing SHM with a frequency of 4.00 Hz and amplitude 1.80 cm. How long does it take the part to go from x = 0 to x = -1.80 cm ?

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Textbook Question

The displacement of an oscillating object as a function of time is shown in Fig. E14.4. What is (a) the frequency? (b) the amplitude?

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