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Advanced Physics
A) The data points you put on the plot (T2 vs. m) should form a straight line. Draw the best-fit line on your plot. Calculate the slope of the line (remember that slope = rise/run). Show your calculation in the space below, and round the result to 3 sig figs. slope = ____________________ B)Consider the theoretical equation for the period of a vertical mass-spring system shown below. Square both sides of the equation so you have T2 as a function of m. Notice how the relationship between T2 and m is linear (this is why a straight line fit the data so well before). The constant in front of m is the slope of the line! Use this to determine the force constant of the spring, k in units of Newtons per meter (N/m). k = ___________________________ N/m

A) The data points you put on the plot (T2 vs. m) should form a straight line. Draw the best-fit line on your plot. Calculate the slope of the line (remember that slope = rise/run). Show your calculation in the space below, and round the result to 3 sig figs. slope = ____________________ B)Consider the theoretical equation for the period of a vertical mass-spring system shown below. Square both sides of the equation so you have T2 as a function of m. Notice how the relationship between T2 and m is linear (this is why a straight line fit the data so well before). The constant in front of m is the slope of the line! Use this to determine the force constant of the spring, k in units of Newtons per meter (N/m). k = ___________________________ N/m

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A) The data points you put on the plot (T2 vs. m) should form a straight line. Draw the best-fit line on your plot. Calculate the slope of the line (remember that slope = rise/run). Show your calculation in the space below, and round the result to 3 sig figs.

slope = ____________________

B)Consider the theoretical equation for the period of a vertical mass-spring system shown
below. Square both sides of the equation so you have T2 as a function of m. Notice how the
relationship between T2 and m is linear (this is why a straight line fit the data so well before).
The constant in front of m is the slope of the line! Use this to determine the force constant of
the spring, k in units of Newtons per meter (N/m).
k = ___________________________ N/m

**Table 1. Simple Harmonic Motion Data** | Hanging Mass, m (g) | Period, T (s) | m (kg) | T² (s²) | |----------------------|---------------|--------|---------| | 50 | 0.812 | 0.05 | 0.659 | | 100 | 0.919 | 0.1 | 0.844 | | 150 | 1.076 | 0.15 | 1.158 | | 200 | 1.232 | 0.2 | 1.518 | | 250 | 1.320 | 0.25 | 1.742 | | 300 | 1.406 | 0.3 | 1.977 | This table presents data relevant to simple harmonic motion, showing the relationship between the mass of an object and its oscillation period. - **Hanging Mass, m (g):** The mass of the weight in grams. - **Period, T (s):** The time it takes for one complete oscillation in seconds. - **m (kg):** The mass converted to kilograms. - **T² (s²):** The square of the period, demonstrating how period changes with mass, useful for analyzing the dynamics of the motion. This data can be used to explore principles of harmonic motion and verify the dependence of the period on mass.
Transcribed Image Text:**Table 1. Simple Harmonic Motion Data** | Hanging Mass, m (g) | Period, T (s) | m (kg) | T² (s²) | |----------------------|---------------|--------|---------| | 50 | 0.812 | 0.05 | 0.659 | | 100 | 0.919 | 0.1 | 0.844 | | 150 | 1.076 | 0.15 | 1.158 | | 200 | 1.232 | 0.2 | 1.518 | | 250 | 1.320 | 0.25 | 1.742 | | 300 | 1.406 | 0.3 | 1.977 | This table presents data relevant to simple harmonic motion, showing the relationship between the mass of an object and its oscillation period. - **Hanging Mass, m (g):** The mass of the weight in grams. - **Period, T (s):** The time it takes for one complete oscillation in seconds. - **m (kg):** The mass converted to kilograms. - **T² (s²):** The square of the period, demonstrating how period changes with mass, useful for analyzing the dynamics of the motion. This data can be used to explore principles of harmonic motion and verify the dependence of the period on mass.
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