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.   What is the force constant of the spring

Principles of Physics: A Calculus-Based Text
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Chapter13: Mechanical Waves
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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.

 

  • What is the force constant of the spring?

 

The image depicts a graph of a sinusoidal wave, representing a periodic motion. Here's a detailed 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 +3.0 cm and -3.0 cm, suggesting an amplitude of 3.0 cm.
- The graph shows two full cycles within the time frame.

**Key Points:**
- Each cycle extends for 0.5 seconds, indicating a frequency of 2 Hz since there are two cycles per second.
- The wave crosses the horizontal axis (equilibrium position) at intervals of approximately 0.25 seconds, 0.75 seconds, and 1.25 seconds.
- The peaks occur at approximately 0.25 and 0.75 seconds, while the troughs occur at approximately 0.5 and 1.0 seconds.

This graph is an excellent representation of simple harmonic motion and can be used to illustrate concepts such as amplitude, period, frequency, and phase in wave mechanics.
Transcribed Image Text:The image depicts a graph of a sinusoidal wave, representing a periodic motion. Here's a detailed 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 +3.0 cm and -3.0 cm, suggesting an amplitude of 3.0 cm. - The graph shows two full cycles within the time frame. **Key Points:** - Each cycle extends for 0.5 seconds, indicating a frequency of 2 Hz since there are two cycles per second. - The wave crosses the horizontal axis (equilibrium position) at intervals of approximately 0.25 seconds, 0.75 seconds, and 1.25 seconds. - The peaks occur at approximately 0.25 and 0.75 seconds, while the troughs occur at approximately 0.5 and 1.0 seconds. This graph is an excellent representation of simple harmonic motion and can be used to illustrate concepts such as amplitude, period, frequency, and phase in wave mechanics.
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