Can some help me find the slope, spring constant, percentage difference, and question 5. And someone check my work because my percentage difference is way to high at 59 percent

Simple Harmonic Motion Name: 1. Objective Study oscillatory motion of a mass suspended by a spiral spring. 2. Apparatus Spring, supporting rod, clamp, stopwatch, and a set of slotted weights. 3. Theory A mass suspended by a light spring will execute vibrations if its restoring force opposes its displacement from an equilibrium position. This kind vibration is an example of simple harmonic motion. A more sophisticated study of this motion reveals: t = 2 n where t is the period of the vibration, M is the suspended mass, and k is the spring constant. This equation expresses the relation between the vibration period of the spring and the amount of mass attached to the spring. By squaring both sides of the equation one can get: 12 = (472/k) M Let to be y, M be x, and (47 /k) be m, then the above equation becomes y = mx, that is in form of the equation of a straight line, where m is the slope. By plotting the graph, the slope can be obtained, and then the spring constant k can be found. 4. Preparation 4.1 Read the following article to get some idea about a simple pendulum https://en.wikipedia.org/wiki/Oscillation https:/www.khanacademy.org/science/ap-physics-1/simple-harmonic-motion-ap/spring-mass-systems- ap/a/simple-harmonic-motion-of-spring-mass-systems-ap 4.2 Watch the following videos to see a demonstration for this lab. https://www.youtube.com/watch?v=FJBPNJR2QJU 1EGG 131L, Lab 9 Manual, 80 points https://www.khanacademy.org/science/ap-physics-1/simple-harmonic-motion-ap/spring-mass- systems-ap/v/period-dependance-for-mass-on-spring 5. Procedure 5.1 Attach a mass of 0.2 kg to the spring, and make it vibrating (oscillating). Measure the time T elapsed for 10 small-amplitude oscillations. To obtain the reliable value of T, avoid pendulum-like swinging of the spring, or bumping of the weights. Record your data in the following table. The time t for a single vibration then is 0.1 T. 5.2 Repeat the same procedure for the different masses as indicated in the table. 5.3 Plot a graph using t' as y-axis, and M as x-axis. Find the slope. From the slope find the k; and then compare it with the average value of k from experiment 5 to find the percentage difference. 2EGG 131L, Lab 9 Manual, 80 points Lab Report 1. Purpose (8 points) study and understand Oscillatory motion or a mass suspended by a spiral spring. Obtain the spiring constant through hookes law, pentarival enrosy, and Oscillarun motion. 2. Data (24 points) Trial Mass T t t2 0.2 kg 10 sec |10/ 107 1 5 2 0.3 kg 12 sec 12/ 10:1.25 1. 4 4 1 , 2 3 0.4 kg 14. 2 5 cc 1.42 2. 015 2 2.345 2 A 0.5 kg 15.3 Sec | 1. 53 5 16. 2 sec | 1. 62 5 | 2. 62 5 2 UI 0.6 kg 6 0.7 kg 48. 1 sce 1.8/ s | 3. 275 2 0.8 kg 19. 3 sec .1:93 5 3. 73 5 2 100 0.9 kg 20. 5 sec 2.65 5 4.2 4. 97 52 9 1.0 kg 22. 3 See| 2.23 5 1.1 kg 23. 0sec 2.35 5. 30 52 10 24. I see. 2. 41 s 5. 80 52 11 1.2 kg 25.4 Sec . 2.54 s 6.45 52 12 1.3 kg WEGG 131L, Lab 9 Manual, 80 points 2. Graph (28 points) 6 lime savored ( sec ) 5 14 3 2 X . 2 - 4 . 6 . 7 1.0 1. 1 1. 2 1. 3 1.9 1: 5 M Mass ( Kq) 4EGG 131L, Lab 9 Manual, 80 points 3. Computation (10 points) Find the slop from the above graph, and then find the spring constant from the slope. PI ( 1 , .5 ) P2 ( 1.4 6.8) Slope = 12 - yl 6.8 -.5 _ 6.3 X2 - X1 - 1.4 -. 1 1.3 = 4. 84 Nlm 4. Conclusion (10 points) This is the same spring used in Lab 5. Find the percentage difference between the spring constant in this lab and the one found in Lab 5 (there are 2 values of spring constants in Lab 5 use the average). Las 5 K,, = 8.3 nim KI - K2 4.3 - 8.25 Lab s KA = P. Bin/m 1/2 ( Kitk2 ) X100 - 1 12 ( 8. 85 + 4 2 ) X100 Lab 9 K1 = 4. in/m Lab 5 KAverages 1.85 5. Theory related to a spring (20 points) You need to show the procedure to solve the following problem. Assume the spring used in this lab has a spring constant of 10 N/m. If a mass of 1 1b. is attached, and the mass pulls for 5 inches. When the mass is released what will be its maximum speed going up in m/s, and what will be its maximum acceleration in m/s? UT