Objective: Determine the effect of the length the pendulum on its frequency while we keep constant the mass (m) and the amplitude (0) (see below figure). amplitude (angle) mass (m) Table 1. Simple Pendulum - Length variation Time taken for 5 oscillations Length Period (T) Frequency ( t3 (s) Average (L) (m) ti (s) t2 (s) time, t (s) (s) (Hz) 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Add the questions and the respective answers at the end of the Discussion section of the lab report. Graph the data using Excel. Note: If the relation between variables is not linear, you do NOT need to fit the data with a linear equation. Just use a trend line to connect the points with the best curve. 1. Plot frequency (f) (y-axis) vs. length (L) (x-axis). Is the relation between frequency and length linear?2. Plot frequency (f) (y-axis) vs. the inverse of length (1/L) (x-axis). Is the relation between frequency and the inverse of length linear? 3. Plot frequency square (f2) (y-axis) vs. inverse of length (1/L) (x-axis). What is the relationship between frequency square and the inverse of length? . Find the experimental equation that correlates frequency square (f2) and the inverse of length (1/L) using Excel. Write the final equation with the appropriate variables (f2 and 1/L ). 5. What are the value and units of the slope? 6. Compare the experimental equation determined by using excel for f2 vs. 1/L with the theoretical equation that correlates f2 vs. 1/L: f2 8 1 4TT2 L (Theoretical equation)7. What part of the theoretical equation is equal to the slope of the experimental equation? 8. Calculate the experimental acceleration of gravity (g) using the relation found in Q7. Is this value close to the theoretical value of the acceleration of gravity (gtheoretical = 9.8 m/s2) 9. Use the given equation to calculate the percentage of error: %Error = Jexperimental - 9theoretical . 100 I theoretical Note: Do not forget to add the inverse length (1/L) and the frequency squared (f?) data to Table 1