A 2.38 kg ball is attached to an unknown spring and allowed to oscillate. The figure shows a graph of the ball's position x as a function of time t. For this motion, what is the period? What is the frequency? What is the angular frequen

Physics for Scientists and Engineers
10th Edition
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter17: Superposition And Standing Waves
Section: Chapter Questions
Problem 10P: A standing wave is described by the wave function y=6sin(2x)cos(100t) where x and y are in meters...
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A 2.38 kg ball is attached to an unknown spring and allowed to oscillate. The figure shows a graph of the ball's position x as a function of time t.

  • For this motion, what is the period?
  • What is the frequency?
  • What is the angular frequency?

 

The image presents a graph of a sinusoidal wave. Here's a detailed explanation:

**Graph Description:**

- **Axes:**
  - The horizontal axis is labeled as \( t(s) \), indicating time in seconds.
  - The vertical axis is labeled as \( x(cm) \), indicating displacement in centimeters.

- **Wave Characteristics:**
  - The wave oscillates between +3 cm and -3 cm on the vertical axis, showing the maximum and minimum displacement.
  - At \( t = 0 \), the wave displacement is at 0 cm.
  - The wave completes one full cycle (from crest to crest) between \( t = 0 \) s and \( t = 1.0 \) s. This represents the period of the wave.
  - The midpoints of the wave at \( t = 0.50 \) s and \( t = 1.0 \) s indicate points where the displacement crosses the time axis, moving upward through zero (positive slope).

- **Cycles:**
  - The graph shows two full cycles of the wave, each cycle lasting 1 second.

This sinusoidal wave graph can be used in educational materials to demonstrate concepts such as wave amplitude, period, and frequency.
Transcribed Image Text:The image presents a graph of a sinusoidal wave. Here's a detailed explanation: **Graph Description:** - **Axes:** - The horizontal axis is labeled as \( t(s) \), indicating time in seconds. - The vertical axis is labeled as \( x(cm) \), indicating displacement in centimeters. - **Wave Characteristics:** - The wave oscillates between +3 cm and -3 cm on the vertical axis, showing the maximum and minimum displacement. - At \( t = 0 \), the wave displacement is at 0 cm. - The wave completes one full cycle (from crest to crest) between \( t = 0 \) s and \( t = 1.0 \) s. This represents the period of the wave. - The midpoints of the wave at \( t = 0.50 \) s and \( t = 1.0 \) s indicate points where the displacement crosses the time axis, moving upward through zero (positive slope). - **Cycles:** - The graph shows two full cycles of the wave, each cycle lasting 1 second. This sinusoidal wave graph can be used in educational materials to demonstrate concepts such as wave amplitude, period, and frequency.
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