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A box is attached to a spring and can move along a frictionless, horizontal surface according to this graph of acceleration vs time. Additional information: A Weight of box= 50 N 6 4 1) What is the angular frequency of oscillation? 2) What is the maximum displacement from the equilibrium position of the spring? 3) Write out the position vs time, velocity vs time, and acceleration vs time equations that describe the G 4. 6. 10 (In elude unite) Acceleration (cm/s?}

A box is attached to a spring and can move along a frictionless, horizontal surface according to this graph of acceleration vs time. Additional information: A Weight of box= 50 N 6 4 1) What is the angular frequency of oscillation? 2) What is the maximum displacement from the equilibrium position of the spring? 3) Write out the position vs time, velocity vs time, and acceleration vs time equations that describe the G 4. 6. 10 (In elude unite) Acceleration (cm/s?}

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### Physics of Harmonic Motion: Analyzing a Box-Spring System A box is attached to a spring and can move along a frictionless, horizontal surface according to this graph of acceleration vs time. #### Additional Information: - **Weight of box:** 50 N ### Questions to Consider: 1. **What is the angular frequency of oscillation?** 2. **What is the maximum displacement from the equilibrium position of the spring?** 3. **Write out the position vs time, velocity vs time, and acceleration vs time equations that describe the motion of this box.** (Include units) 4. **What is the maximum spring potential energy?** 5. **What is the magnitude of the maximum velocity of the box?** ### Choose from the Labeled Points (A-H): There may be only one point, more than one point, or none that correctly answer the questions below. If there are no points, write “none.” 6. **Where is the magnitude of the velocity maximum?** 7. **Where is the displacement of the box zero?** 8. **Where is the spring potential energy negative?** ### Detailed Explanation of the Provided Graph: - The graph is a plot of acceleration (in cm/s²) on the y-axis vs time (in seconds) on the x-axis. - The curve oscillates between 6 cm/s² and -7 cm/s². - Points A-H are labeled on the graph at various times: - **A** around 2.3 seconds - **B** around 3.5 seconds - **C** just before 5 seconds - **D** just after 5 seconds - **E** at 6 seconds - **F** around 7 seconds - **G** around 8 seconds - **H** at approximately 7.5 seconds This graph depicts a sinusoidal oscillation which is typical of simple harmonic motion (SHM). ### Application and Analysis: To fully analyze this system: - **Angular Frequency (\( \omega \))** can be derived from the period of the oscillation observed in the graph. - **Maximum Displacement (\( x_{max} \))** is related to the maximum acceleration using \( a_{max} = \omega^2 x_{max} \). - **Equations of Motion** can be determined from the sinusoidal nature of the oscillation
Transcribed Image Text:### Physics of Harmonic Motion: Analyzing a Box-Spring System A box is attached to a spring and can move along a frictionless, horizontal surface according to this graph of acceleration vs time. #### Additional Information: - **Weight of box:** 50 N ### Questions to Consider: 1. **What is the angular frequency of oscillation?** 2. **What is the maximum displacement from the equilibrium position of the spring?** 3. **Write out the position vs time, velocity vs time, and acceleration vs time equations that describe the motion of this box.** (Include units) 4. **What is the maximum spring potential energy?** 5. **What is the magnitude of the maximum velocity of the box?** ### Choose from the Labeled Points (A-H): There may be only one point, more than one point, or none that correctly answer the questions below. If there are no points, write “none.” 6. **Where is the magnitude of the velocity maximum?** 7. **Where is the displacement of the box zero?** 8. **Where is the spring potential energy negative?** ### Detailed Explanation of the Provided Graph: - The graph is a plot of acceleration (in cm/s²) on the y-axis vs time (in seconds) on the x-axis. - The curve oscillates between 6 cm/s² and -7 cm/s². - Points A-H are labeled on the graph at various times: - **A** around 2.3 seconds - **B** around 3.5 seconds - **C** just before 5 seconds - **D** just after 5 seconds - **E** at 6 seconds - **F** around 7 seconds - **G** around 8 seconds - **H** at approximately 7.5 seconds This graph depicts a sinusoidal oscillation which is typical of simple harmonic motion (SHM). ### Application and Analysis: To fully analyze this system: - **Angular Frequency (\( \omega \))** can be derived from the period of the oscillation observed in the graph. - **Maximum Displacement (\( x_{max} \))** is related to the maximum acceleration using \( a_{max} = \omega^2 x_{max} \). - **Equations of Motion** can be determined from the sinusoidal nature of the oscillation
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