PHY122_Hookes_Law_worksheet_2023-1

k s = SPRINGS AND OSCILLATORS – LAB WORKSHEET Name: Partners: TA: OBJECTIVE DATA Experiment #1 – static spring Experiment #2 – rubber band Mass (g) Displacement 1 (cm) (increasing mass) Displacement 2 (cm) (decreasing mass) Displacement 1 (cm) (increasing mass) Displacement 2 (cm) (decreasing mass) 1. Experiment #1: Is the linear relationship F ( x ) = − k s x a good model to fit the data? Reflect in the Discussion & Conclusion whether or not the spring obeys Hooke’s Law and explain your reasoning based on how well the model fits the data. More specifically, what about the slope tells you whether or not Hooke’s Law is valid? 2. Experiment #2: Is the linear relationship F ( x ) = − k s x a good model to fit the data? Reflect in the Discussion & Conclusion whether or not the rubber band obeys Hooke’s Law and explain your reasoning based on how well the model fits the data. More specifically, what about the slope ... ? 1

3 Experiment #3 – A vs. ω !! Note: mass on the hanger is constant (500 g) Experiment #4 – dynamic spring !! Note: amplitude is constant(ish) ( ∼ 1-2 cm) Amplitude A (cm) Ang. Frequency ω (rad/s) Mass (g) Ang. Frequency ω (rad/s) 1 2 3 4 5 – – Record the total mass of the hanger and additional mass of 200g on the hanger: m h = g. 1. Refer to Eq. (13) in the manual; the equation is analogous to y ( x ) = mx + b . Use the slope of your T 2 ( m ) graph to determine the dynamic spring constant k d . Show your work with units. 2. Use the y-intercept to determine the effective mass of the spring, m 0 . Show your work with units. 3. Calculate the percent difference between k d and k s . 4. Calculate the percent discrepancy between m 0 and 1 m s . (Note: m 0 - is effective mass of the spring found using the graph; m s - is theoretical mass of the spring found using the balance; m h - is the total mass of the hanger and 200g added to the spring to decompress it. ) 2 % difference = | k d − k s | k d + k s 2 × 100% % discrepancy = | m − 0 ( m + m ) 1 3 s h | ( 1 × 100% 3 m + m ) s h