Lab_6_Pendulum_and_SHM_S23

Lab 6 (online): Pendulum and Simple Harmonic Motion (Friday, 4-14-2023) (due 11:59 pm, Wednesday, April 19, 2023. Not a formal report) Pendulum Lab 2.03 T 2 = 4 π 2 g l Procedures For this experiment, we chose the initial angle at 12 degrees and , measured the time for each oscillation at each length . 1. Prove the independence of T or ω on mass (with fixed L and small angle (less than 15 deg) but 3 different masses) 2. Prove the independence of T or ω on initial angle or amplitude (with fixed L and small angle (less than 15 deg) 3. Find the gravitational acceleration on the earth surface, g (make a table) (a) fix a mass (e.g. 0.5 kg) (b) record T for each l ( l =0.2, 0.3, 0.4, 0.6, 0.8, and 1.0 m) (c) calculate T 2 (d) plot T 2 (y-axis) against l (x-axis) (e) find the slope of the plotted straight line (f) calculate g, g = 4 π 2 /slope (why?) Table 1 Period measurement for different string length l (m) T (s) T 2 (s 2 ) 0.2 0.8 0.64 0.3 1.1 1.21 0.4 1.2 1.44 T 2 l

0.6 1.5 2.40 0.8 1.8 3.24 1.0 2 4 Slope = __4.2 ________ (s 2 /m) g = ______9.39 ___(m/s 2 ) error% = (9.8- 9.39/9.8 )*100 = 4.18% ___________ FOR THE SLOPE WE CAN USE RISE/RUN USING THE POINTS (0.2, 0.64) AND (1, 4) WE HAVE 4-0.64/1-0.2=4.2 WE CAN FIND g using g = 4 π 2 slope =9.39m/s^2 4. Find the gravitational acceleration on the moon, g moon (just use one measurement, multiple measurements in step 3 will reduce the experimental error). Find g moon . l = ___0.70____ (m) T = ____3.7__ (s) g moon 2__(m/s 2 ) gmoon true value . =9.8m/s^2/6=1.63m/s^2.We can see that the calculated gmoon value is greater than the true value 1.6m/^2. g = 4 π 2 T 2 l 5. Measure T for three angles (fix mass and L and measure T with 3 initial angles (5, 10 and 30 deg). Are the values of T(5) and T (10) very close? What about T(30)? Explain if you find the value that differs from T(5) or T(10). Table 2 Period measurement for different angles. Initial Angle (deg) Period (s) 5 1.55 10 1.52 30 1.6