Simple Harmonic Motion

Physics Laboratory explanation Simple likeable trend cause the suck up perpetual Aim of test The objective of this experiment is 1. To study the simplistic agreeable act of a bulk- dancing placement 2. To estimate the force constant of a flood Principles involved A level or vertical plurality- organise carcass skunk perform transparent harmonic relocation as shown below. If we k this instant the period (T) of the intercommunicate and the great deal (m), the force constant (k) of the kick back can be determined. pic Consider pull the mass of a horizontal mass- arising constitution to an extension x on a table, the mass subjected to a restoring force (F=-kx) utter by Hookes Law.If the mass is now released, it will move with acceleration (a) towards the equalizer position. By Newtons atomic number 16 law, the force (ma) acting on the mass is equal to the restoring force, i. e. ma = -kx a = -(k/m)x -(1) As the movement continues, it performs a simple harmonic motion with angular velocity (? ) and has acceleration (a = -? 2x). By comparing it with equation (1), we pack ? = v(k/m) Thus, the period can be equal as follows T = 2? /? T = 2? x v(m/k) T2 = (4? 2/k) m (2)From the equation, it can be seen that the period of the simple harmonic motion is independent of the amplitude. As the result similarly applies to vertical mass- chute system, a vertical mass- take form system, which has a smaller frictional effects, is employ in this experiment. Apparatus Slotted mass (20g)x 9 Hanger (20g)x 1 Springx 1 regress stand and clampx 1 Stop watchx 1 G-clampx 1 Procedure 1. The apparatuses were strike out up as shown on the right. 2. No slotted mass was originally regurgitate into the hanger and it was set to thrill in lessen amplitude. 3.The period (t1) for 20 make out oscillations was metrical and disced. 4. Step 3 was repeated to scram a nonher record (t2). 5. Steps 2 to 4 were repeated by adding one slotted mass to the hanger all(pr enominal) judgment of conviction until all of the nine given all over masses have been employ. 6. A chart of the square of the period (T2) against mass (m) was plotted. 7. A best-fitted line was drawn on the graphical record and its gear was measured. Precaution 1. The oscillations of the shrink were of moderate amplitudes to reduce fractures. 2. The oscillations of the take a hop were conservatively initiated so that the wince did not swing to chink unblemished results. . The take form used was carefully chosen that it could perform 20 oscillations with elfin decay in amplitude when the hanger was put on it, and it was not over-stretched when all the 9 slotted masses were put on it. This could find accurate and tested results. 4. The experiment was carried give away in a place with dinky air movement (wind), in prepare to reduce baseball swing of the resound during oscillations and errors of the experiment. 5. The organise was clamped tightly so that the co nfine did not slide during oscillation. It reduced energy spillage from the outset and ensured accurate results. . A G-clamp was used to attach the stand firmly on the bench.This reduced energy loss from the spring and ensured accurate results. Results Hanger and slotted mass 20 periods / s One period (T) T2 / s2 (m) / kg / s t1 t2 Mean (0. 1s) (0. s) = (t1 + t2) / 2 0. 02 5. 0 5. 4 5. 2 0. 26 0. 0676 0. 04 6. 0 6. 0 6. 0 0. 3 0. 09 0. 06 7. 0 7. 0 7. 0 0. 35 0. 1225 0. 08 7. 8 7. 8 7. 8 0. 9 0. 1521 0. 10 8. 6 8. 6 8. 6 0. 43 0. 1849 0. 12 9. 4 9. 5 9. 45 0. 4725 0. 22325625 0. 14 10. 1 10. 1 10. 1 0. 505 0. 255025 0. 16 10. 5 10. 4 10. 45 0. 5225 0. 27300625 0. 8 11. 1 11. 3 11. 2 0. 56 0. 3136 0. 20 11. 9 12. 0 11. 95 0. 5975 0. 35700625 Calculations and Interpretation of results pic From equation (2), the run of the graph is equal to (4? 2/k), i. e. 1. 5968 = 4? 2/k k = 4? 2/1. 5968 ? 24. 723 Nm-1 ?The force constant of the spring is 24. 723 Nm-1. Sourc es of error 1. The spring swung during oscillations in the experiments. 2.As the amplitudes of oscillations were small, there was impediment to determine whether an oscillation was effected. 3. Reaction time of commentator was involved in time-taking. 4. get-up-and-go was lost from the oscillations of the spring to resonance of the spring. localize of Accuracy Absolute error in time-taking = 0. 1s Hanger and slotted mass (m) / kg 20 periods / s Relative error in time-taking t1 t2 (0. s) (0. 1s) t1 t2 0. 02 5. 0 5. 4 2. 00% 1. 85% 0. 04 6. 0 6. 0 1. 67% 1. 67% 0. 06 7. 0 7. 0 1. 3% 1. 43% 0. 08 7. 8 7. 8 1. 28% 1. 28% 0. 10 8. 6 8. 6 1. 16% 1. 16% 0. 12 9. 4 9. 5 1. 06% 1. 05% 0. 14 10. 1 10. 1 0. 990% 0. 990% 0. 6 10. 5 10. 4 0. 952% 0. 962% 0. 18 11. 1 11. 3 0. 901% 0. 885% 0. 20 11. 9 12. 0 0. 840% 0. 833% Improvement 1. The spring should be initiated to oscillate as vertical as possible to prevent jive of the spring, which would cause energy loss from t he spring and give inaccurate results. 2. some(prenominal) watch overrs could observe the oscillations of the spring and determine a more accurate and reliable result that whether the spring has completed an oscillation. 3. The time taken for oscillations should be taken by the same observer. This allows more reliable results as error-error cancellation of reaction time of the observer occurs. 4. The spring used should be make of a material that its resonance frequence is vexed to match. Discussion In this experiment, several(prenominal) assumptions were made. First, it is assumed that the spring used is weightless and resonance does not occur.Furthermore, it is assumed that no energy is lost from the spring to stunnedgo the air resistance. Besides, it is assumed that no swinging of the spring occurs during the experiment. In addition, there were difficulties in carrying out the experiment. For timing the oscillation, as the spring oscillates with moderate amplitude, it was h ard to determine if a complete oscillation has been accomplished. Added to this, in picture the best-fitted line, as all the points do not join to form a groovy line, there was a little difficult encountered while drawing the line.Nevertheless, they were all solved. Several observers observed the oscillations of the spring and determined a more reliable result that whether the spring has completed an oscillation. For the best-fitted line, computer was employed to obtain a reliable graph. Conclusion The mass-spring system performs simple harmonic motion and the force constant of the spring used in this experiment is 24. 723 Nm-1. A graph of T2 against m Square of the period (T2) picSimple Harmonic MotionShanise Hawes 04/04/2012 Simple Harmonic Motion Lab Introduction In this 2 part science laboratory we sought out to demonstrate simple harmonic motion by observe the behavior of a spring. For the first part we needed to observe the motion or oscillation of a spring in separate to find k, the spring constant which is commonly expound as how stiff the spring is. victimisation the equation Fs=-kx or, Fs=mg=kx where Fs is the force of the spring, mg make ups mass times gravity, and kx is the spring constant times the distance, we can mathematically seclude for the spring constant k.We can also graph the data still and the slope of the line will reflect the spring constant. In the abet part of the lab we used the equation T=2? mk, where T is the period of the spring. After work out and graphing the data the x-intercept represented k, the spring constant. The spring constant is technically the measure of centering of the spring. entropy mass of weight translation m (kg) x (m) 0. 1 0. 12 0. 2 0. 24 0. 3 0. 36 0. 4 0. 48 0. 5 0. 60We began the experiment by placing a coiled spring on a clamp, creating a spring system. We past measured the distance from the bottom of the suspended spring to the floor. Next we placed a 100g weight on the bottom of t he spring and and so measured the displacement of the spring receivable to the weight . We repeated the procedure with 200g, 300g, 400g, and 500g weights. We past placed the recorded data for for each one trial into the equation Fs=mg=kx. For case 300g weight mg=kx 0. 30kg9. 8ms2=k0. 36m 0. 30kg 9. 8ms20. 36m=k 8. 17kgs=kHere we graphed our collected data. The slope of the line verified that the spring constant is approximately 8. 17kgs. In the present moment part of the experiment we suspended a 100g weight from the bottom of the spring and pulled it very(prenominal) slightly in order to set the spring in motion. We then used a timer to time how pertinacious it took for the spring to make one complete oscillation. We repeated this for the 200g, 300g, 400g, and 500g weights. Next we divided the times by 30 in order to find the fair(a) period of oscillation. We then used the equation T2=4? mk to mathematically isolate and find k. Lastly we graphed our data in order to find the x-intercept which should represent the value of k. Data Collected Derived Data mass of weight time of 30 osscillation avg osscilation T T2 m (kg) t (s) t30 (s) T2 s2 0. 10 26. 35 0. 88 0. 77 0. 20 33. 53 1. 12 1. 25 0. 30 39. 34 1. 31 1. 72 0. 40 44. 81 1. 49 2. 22 0. 50 49. 78 1. 66 2. 76 waiver back to our equation T2=4? 2mk .We open up the average period squared and the average mass and set the equation up as T2m=4? 2k. Since T2 is our change in y and m is our change in x, this also helped us to find the slope of our line. We got T2m equals approximately 4. 98s2kg. We now have 4. 98s2kg= 4? 2k. Rearranging we have k=4? 24. 98s2k= 7. 92N/m. Plotting the points and observing that the slope of our line is indeed approximately 4. 98 we see that the line does continue the x-axis at approximately 7. 92. Conclusion introductory to placing any additional weight onto our spring we measured the length of spring to be 0. 8m. So if we hooked an identical spring and an additi onal 200g the elongation of our total spring would be approximately 0. 8m accounting for in two ways our spring and the . 24m the additional weight added. However, I believe the additional weight of the second spring would slightly elongate the sign spring bringing it roughly over a meter. Since our spring elongation has just about tripled I believe that an effective spring constant would be triple that of what we name it to be initially, making a mod spring constant of 24. 51kgs