5BL Lab 4 Assignment Submission Template - F23v2

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Jan 9, 2024

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5±!L !Lab 4 ²ssignment aylynn, ²shley, and Sama, 10/30/23, !Lab °1, ±ench 10 C\RhUK]n ZPfSi]nSis\RhUKSI HSISISi]n[Qg your rUKspo]nsUKs o]n UKHQG\Rh s[lSiSIUK, sHvUK t\RhSis Hs H 7±" ZPfSi[lUK H]nSI up[loHSI Sit to your #rHSIUKsQGopUK HssSi[Qg]n\mUK]nt.

2 1. ³escribe your experimental setup, including how you are able to measure the experimental spring constants. ´or this experiments set up we first measured the length of our unstretched spring and then attached our spring to a large ruler using a hook so it’s hanging. Then we attached a weight to the bottom end of the spring, and measured the change in length from when the spring is not stretched at all verse when the weight is pulling down on it. We did this for 2 different weights then used the data collected to solve for k using the equation k=(m1-m2)/(x1-x2)*g. .RYNfm`jjP the masses used and rest lengths of the springs in each mass-spring system. ±EbiNnnbiEmmRY the spring constants and theoretical angular frequencies for your 4 experimental setups, and include an example calculation of theoretical angular frequency below the table. 7KFVV±=8SUNQL =8\VWJP >9UNKFOV" 8oGHl ?6JXYsXYs % P ² % ²³³L ?6JXYsXYs &$ P ´ % ´³³L <UVpWXrRNOSTPL % N ² % µ¶· ¸ 83¹P [ ² % !·¸HP շ WMJRU\ % ³·¶² UKFI¹V [ ´ % µ¶HP շ WMJRU\ % ³·¸µ UKFI¹V <UVpWXrRNOSTPL &$ N ´ % ¸! 83¹P [ ² % ´º·µHP շ WMJRU\ % ³·» UKFI¹V [ ´ % ¸º·µHP շ WMJRU\ % ³·º UKFI¹V

3 2. .RYNfm`jjP the time required to complete 10 periods of oscillation for each setup. ±fm`cj]tgnnmmRY the observed angular frequency from these times and the percentage error from these and your theoretical predictions in question 1. µompare results to your prediction. ³iscuss possible sources of error, and which source(s) you think is/are most likely and why. ±e specific. Our results reflect our predictions of having the mass 2, the heavier mass, take a longer amount of time to complete ten oscillations for both springs (11.35 > 7.5, 12.62 > 9.09). µonversely, the times we calculated were different than our observed data, but error remained below 15% for each trial. Possible sources of error include releasing the weights from different tensions i.e. pulling it down at different by different lengths, starting and stopping the stopwatch at inaccurate times (too early or too late)--especially late reaction time at 8 am, and our springs having slight kinks in them, 7KFVV±=8SUNQL =8\VWJP >9UNKFOV" 0xpHrLmHnt ?6JXYsXYs % P ² % ²³³L ?6JXYsXYs &$ P ´ % ´³³L <UVpWXrRNOSTPL % N ² % µ¶· ¸ 83¹P ²³>9 % »·º V շ RLGV % ·µ UKFI¹V ¼ /UURU % ²´·»¸¼ ²³>9 % ²²·µº V շ RLGV % º·º¸ UKFI¹V ¼ /UURU % ²²· ¼ <UVpWXrRNOSTPL &$ N ´ % ¸! 83¹P ²³>9 % !·³! V շ RLGV % ¶·!² UKFI¹V ¼ /UURU % ·! ¼ ²³>9 % ²´·¶´ V շ RLGV % ¸·!! UKFI¹V ¼ /UURU % ·! ¼

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4 3. ³escribe your experimental setup for the pendulum (include diagrams as needed). .RYNfm`jjP the lengths of each pendulum you used. ±EbiNnnbiEmmRY the theoretical angular frequency for each length , in the table at right. Include an example calculation below. :5JQIXOXP >9UNKFOV" 8oGHl 3STPLuQRJWXr 8WXrNJVWquNJSTLHRNONJXYs 6JQLWM ² 6 ² % »´·´HP շ WMJRU\ % ³·²µ¶ UKFI¹V 6JQLWM ´ 6 ´ % º»HP շ WMJRU\ % ³·²» UKFI¹V 6JQLWM µ 6 µ % ¸¸HP շ WMJRU\ % ³·´´ UKFI¹V 6JQLWM ¸ 6 ¸ % µµ·ºHP շ WMJRU\ % ³·´! UKFI¹V ´or this experiment we first attached a string to a piece of metal hanging off of our ruler. On the bottom end of the string was a ball. ²fter measuring the length of our spring by using the ruler provided to measure from the hook to the ball we then rocked the pendulum back and forth, and measured the time it took for the ball to go back and forth 10 times. We then completed this for 4 different lengths and used the data collected to solve for each trials angular frequency.

5 4. .RYNfm`jjP the time required to complete 10 periods of oscillation for each setup. ±fm`cj]tgnnmmRY the observed angular frequency from these times and the percentage error from these and your theoretical predictions in question 3. µompare results to your predictions. ³iscuss possible sources of error (and which error(s) you think is/are most likely and why). :5JQIXOXP >9UNKFOV" 8oGHl 6JQLWM ² 6 ² % »´·´ HP ²³>9 % ² ·³² V շ RLGV % µ·¸! UKFI¹V ¼ /UURU % ´¸·¶¶¼ 6JQLWM ´ 6 ´ % º» HP ²³>9 % ²º· » V շ RLGV % µ·!¶ UKFI¹V ¼ /UURU % ´´·´!¼ 6JQLWM µ 6 µ % ¸¸ HP ²³>9 % ²µ·!¸ V շ RLGV % ¸·º³ UKFI¹V ¼ /UURU % ²!·¸º¼ 6JQLWM ¸ 6 ¸ % µµ·º HP ²³>9 % ²´·´² V շ RLGV % º·²¶ UKFI¹V ¼ /UURU % ²¶·»!¼ Our theory values is not very similar to our observed values. Our average % error was roughly 20%. ²ll of our theorized angular frequency value was lower than 0.3 rad/s, but our observed value’s lowest value is 3.49 rad/s Possible sources of error include fluctuations of where the initial starting point was for each oscillations, the incorrect time measurements due to human error, releasing ball before or after the stopwatch started, releasing the ball with an extra force, measuring the lengths incorrectly. This class is also very early (8 ²M), so there may be innate 2