1. The relationship between the period of oscillations and the horizontal displacement, T = f (x) 1,6 1,4 1, 2 1 0,8 0,6 0,4 x, cm 0,2 0,0 5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 .T =f (x) 2. The relationship between the period of oscillations and the mass of the weight, T = f (m) 1,55 1,5 1,45 1,4 1,35 1,3 m, g 1,25 50 100 150 200 250 3003. The relationship between the period of oscillations and the 4. The relationship between the squared period and the mass length of a pendulum, T = f(e) of a spring pendulum, T2 = f (e) N 3,5 1,8 y = 1,5004x + 0,7575... 3 y = 4,2332x + 0,1969. 1,6 R.0,9897 RZ = 0,9857.. .. 1,4 2,5 1,2 2 1 0,8 1,5 0,6 1 0,4 e, m 0,5 0,2 e, m 0 0 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 T =f(1) ... ..... Linear (T =f (1)) . T^2 =f (1) ......... Linear (T^2 =f (1))T, $3 3:5 2:5 H 05 5. The relationship between the squared period and the mass of a spring pendulum, T =f [ml O y = 3,5714: + 0,5025" R2 =_0,905.5 o __ "o "1, kg 0,00 0,05 0,10 0,15 0,20 0,25 030 0,35 6. The relationship between the squared period and the mass ofa spring pendulum, T2 = f [m] 12 10 T3I $2 y = 45,53x- 3,5?51 .- R2=0,S'03 m, kg 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 The mathematical equation describing the period T of a pendulum is: E - is the length of the pendulum and g is the earth's acceleration of gravity. Bv theory, the freefall gravity acceleration close to the surface of the earth in Riga is 9.31 mfsz . 3.5.2. Calculate the relative error in percentage for your average free-fall acceleration and justify your answer. 4. The spring pendulum 4.1. Fix the spring pendulum in the support rod {support rod :- force sensor > the spring on sensor's hook]. 4.2. Find the equilibrium by using a ruler to measure the length towards thetable or floor. 4.3. Displace the weight and let it oscillate. 4.4. Use the Pasco Capstone program to record the data {t = 10 s]. 4.5-. By program's results determinate the period T is}, use "add a coordinates tool" > choose the point ti Align Runs 3:- choose next point > Record periods in Table 4. 4.6. Repeat the same steps 4 more times by keeping vertical displacement constant and increasing the mass of pendulum weight each time. Write the results in Table 4. 4.1". If you know the ayerage period and the mass you can calculate the spring constant k. 4.3.1. What happens to the period of spring when you increase the mass?I Justify your answer! Answer: when you increase the mass then it will increase the period of oscillation. This is because it would be more inertia, and therefore affected by the spring constant. 4.3.2. Analyze the relationship T2 = f [m]. Does your data support the relationship? Make conclusions about the graph. What is the difference between Graph 5 and Graph 6? Justify your answer! 5. SHM equation [displacent = f [time]] 2 5.1. Write the equation for simple harmonic oscillations in the form x = xmm- cos (le t) forthe simple pendulum in Task 2 [Table 23. Table 1: The Period of a simple pendulum with varying horizontal displacement No. Displacement, cm Time, 5 Period, 5 5.45 1,09 5.79 1, 156 5 5.39 1,195 6.44 1 265 12 7.06 1,412 15 6,6 1,32 6,85 1,37 22 6,74 1,348 25 6,59 1,316 10 6,84 1,365 11 35 7,58 1,516 Table 2: The relationship between the period of oscillations and the mass of the weight, T = f (m] No. Mass. g Time, s Period, s 50 6,36 1,272 100 6,91 1,362 150 7,26 1,452 200 7,31 1,462 250 7,57 1,514Table 3: The period of a simple pendulum with varying length. The calculation of free-fall gravity acceleration No. Length, m Time, s Period, s 1 0,19 E m/s 5,16 1,032 1,065024 0,30 7,04294 5,94 1,188 1,411344 0,32 8,39166 6,22 1,244 1,547536 0,39 3,16336 6,83 1,366 1,865956 0,42 3,25131 7,12 1,424 2,027776 3,17691 0,49 7,21 1,442 2,079364 9,30305 0,52 7,81 1,562 2,439844 3,41397 0,58 8,11 1,622 2,630884 0,63 8,70334 8,58 1,716 10 2,944656 8,44628 0,67 8,73 1,746 3,048516 8,67653 Average 8,35694 Relative error, % Table 4: Period of a spring pendulum Mass, 150 g No. Mass, 200 g Mass, 300 g Period, s Period, s Period, 5 1 1,15 1,2 2 2 1,6 1,45 3 2,65 2,05 2,15 3,3 2.55 2,65 3.95 3 3,05 4,55 Average 2,07 2,1 3,29 Table 5: Data to calculate the spring constant No. Mass, kg Average period, s T2, $2 k, N/m 1 0,15 2,07 4,2849 1,382007198 0,20 2,1 4,41 1,790404427 0,30 3,29 10,8241 1,094181066