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Over time, the output values of damped functions decrease. O True O False

Over time, the output values of damped functions decrease. O True O False

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Damped Functions and Their Behavior Over Time #### Statement: **Over time, the output values of damped functions decrease.** #### Answer Choices: - ⭕ True - ⭕ False **Explanation:** Damped functions generally refer to functions whose amplitude decreases over time. This is a characteristic observed in various physical systems, such as oscillating springs or electrical circuits, where energy is progressively lost to friction, resistance, or other damping mechanisms. When analyzing damped functions graphically or mathematically, you'll see that while the function may continue to oscillate, the peaks and troughs of these oscillations diminish in height, approaching zero as time progresses. This decline in amplitude is what indicates that the output values are indeed decreasing over time. ##### Example Graph of a Damped Function: If there were a graph provided, you would typically expect to see a waveform that starts with a high amplitude and then gradually reduces in height, converging towards a central axis. This graphical representation helps visualize how the function's maximum and minimum values decrease over time, confirming the statement's truth.
Transcribed Image Text:### Damped Functions and Their Behavior Over Time #### Statement: **Over time, the output values of damped functions decrease.** #### Answer Choices: - ⭕ True - ⭕ False **Explanation:** Damped functions generally refer to functions whose amplitude decreases over time. This is a characteristic observed in various physical systems, such as oscillating springs or electrical circuits, where energy is progressively lost to friction, resistance, or other damping mechanisms. When analyzing damped functions graphically or mathematically, you'll see that while the function may continue to oscillate, the peaks and troughs of these oscillations diminish in height, approaching zero as time progresses. This decline in amplitude is what indicates that the output values are indeed decreasing over time. ##### Example Graph of a Damped Function: If there were a graph provided, you would typically expect to see a waveform that starts with a high amplitude and then gradually reduces in height, converging towards a central axis. This graphical representation helps visualize how the function's maximum and minimum values decrease over time, confirming the statement's truth.
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