5BL Lab 4 Assignment Submission - W24v2

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University of California, Los Angeles *

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5B

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Physics

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Apr 3, 2024

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5±L Lab 4 ²ssignment [²lejandra °ernandez, Yesenia Lara, ³aitlyn Loo], [02/13/24], [Lab Section ´32], [±ench #7] 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. µescribe your experimental setup, including how you are able to measure the experimental spring constants. .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 % ³´´L %´µ³NL ?6JXYsXYs &$ P ³ % ²´´L% ´µ²NL <UVpWXrRNOSTPL % N ² % ¶µ·· 83¸P [ ² % ·²HP շ WMJRU\ % ¶µ³² UJY¸V [ ³ % ³¹HP շ WMJRU\ % ºµ· UJY¸V <UVpWXrRNOSTPL &$ N ³ % ºµ¶¹ 83¸P [ ² % ¹³HP շ WMJRU\ % »µ²¹ UJY¸V [ ³ % ²!HP շ WMJRU\ % µ» UJY¸V ² meter stick is held up vertically against a metal rod. This rod also supports a horizontal metal bar to which the spring is attached and allowed to vertically hang. ²t the end if the string masses of varying mass are attached. We will then use a stopwatch to measure the periods of oscillations with different increasing values of mass that way we can find a difference in any oscillation changes. ²fter we will change the spring constant (k) by changing (inc/dec) the length of the spring by changing the mass then we can find if this change will cause a change in oscillations since finding angular velocity takes spring constant k and mass m into consideration . meterstick
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. ³ompare results to your prediction. µiscuss possible sources of error, and which source(s) you think is/are most likely and why. ±e specific. These results are pretty in line with our predictions with our largest percent error being 4.3% and lowest being 0.96%. The larger mass of .2kg had a lower observed շ than the smaller mass of .1kg. ² possible source of error could be that the springs have deteriorated and become deformed due to several consecutive years of usage. ²nother possible source of error could be timer discrepancies due to human reaction time which could add a couple seconds. There could also possibly be calculation errors but this is the least likely source of error. 7KFVV±=8SUNQL =8\VWJP >9UNKFOV" 0xpHrLmHnt ?6JXYsXYs % P ² % ³´´L ?6JXYsXYs &$ P ³ % ²´´L <UVpWXrRNOSTPL % N ² % ¶µ·· 83¸P ²´>9 % ²²µ!¶V շ RLGV % ¶µ³» UJY¸V ¼ /UURU % ´µ!»¼ ²´>9 % µ¹³V շ RLGV % ºµ¶· UJY¸V ¼ /UURU % ²µ!¼ <UVpWXrRNOSTPL &$ N ³ % ºµ¶¹ 83¸P ²´>9 % ²´µ·!V շ RLGV % ¶µ!º UJY¸V ¼ /UURU % ³µ»¼ ²´>9 % ºµ»³V շ RLGV % µ³¹ UJY¸V ¼ /UURU % ·µ¹¼
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4 3. µescribe your experimental setup for the pendulum (include diagrams as needed). ² meter stick is held up vertically against a metal rod. This rod also supports a horizontal metal bar to which the string (of varying lengths) of the pendulum is attached. ²t the end if the string a golf ball is attached. .RYNfm`jjP the lengths of each pendulum you used. ±EbiNnnbiEmmRY the theoretical angular frequency for each length , in the table at right. ¶nclude an example calculation below. :5JQIXOXP >9UNKFOV" 8oGHl 3STPLuQRJWXr 8WXrNJVWquNJSTLHRNONJXYs 6JQLWM ² 6 ² % ¶¹ HP շ WMJRU\ % ·µ¹´ UJY¸V 6JQLWM ³ 6 ³ % ¹·HP շ WMJRU\ % ¶µ¹º UJY¸V 6JQLWM ¹ 6 ¹ % ³³ HP շ WMJRU\ % »µ»º UJY¸V 6JQLWM · 6 · % ²³HP շ WMJRU\ % !µ² UJY¸V meterstick
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. ³ompare results to your predictions. µiscuss possible sources of error (and which error(s) you think is/are most likely and why). Our results match our predictions; The shorter the length of the pendulum, the shorter it takes the complete 10 periods of oscillation and the higher the angular frequency. Possible sources of error include human error in timing. Slight delays in starting or stopping the stopwatch will affect the calculated angular frequency. The pendulum may have also been released with some force by the human hand which would increase the angular frequency. The series of calculations could have also increased the error. :5JQIXOXP >9UNKFOV" 8oGHl 6JQLWM ² 6 ² % ¶¹ HP ²´>9 % ²¶µ!² V շ RLGV % ¹µ!¶ UJY¸V ¼ /UURU % µ²·¼ 6JQLWM ³ 6 ³ % ¹· HP ²´>9 % ²³µ·V շ RLGV % ¶µ´º UJY¸V ¼ /UURU % ¶µ»¼ 6JQLWM ¹ 6 ¹ % ³³ HP ²´>9 % ²´µ³³V շ RLGV % »µ²· UJY¸V ¼ /UURU % ºµ!¼ 6JQLWM · 6 · % ²³HP ²´>9 % ºµ³¶V շ RLGV % µ»» UJY¸V ¼ /UURU % ·µ ·¼

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