Textbook Question
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
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Ch 14: Periodic Motion
Chapter 14, Problem 14
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? (c) the period? (d) the angular frequency of this motion?
Verified step by step guidance1
Step 1: Identify the amplitude (A) from the graph. The amplitude is the maximum displacement from the equilibrium position. From the graph, the amplitude is 10 cm.
Step 2: Determine the period (T) of the oscillation. The period is the time it takes for one complete cycle of the oscillation. From the graph, the period is 10 seconds.
Step 3: Calculate the frequency (f) using the relationship f = 1/T. Substitute the period (T) into the equation to find the frequency.
Step 4: Calculate the angular frequency (ω) using the relationship ω = 2πf. Substitute the frequency (f) into the equation to find the angular frequency.
Step 5: Summarize the results: amplitude (A), period (T), frequency (f), and angular frequency (ω).
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Related Practice
Textbook Question
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is (a) at its highest point.
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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? (c) the period? (d) the angular frequency of this motion?
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Textbook Question
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Textbook Question
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.
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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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