Simple Harmonic Motion Essay, Research Paper

Object:

The aim of this lab is to obtain the spring invariable by utilizing the simple harmonic gesture of the spring-mass system. Once the spring invariable is obtained it is to be compared to the spring invariable obtained by Hooke? s Law.

Procedure:

1 ) Using a metre stick step the distance from the affiliated point of the spring to the terminal of the spring, at this clip there is to be no mass on the spring. Once this measuring is obtained the elongations can be calculated by deducting the new measurings from this first measuring.

2 ) Add a weight to the spring and record the distance. The new distance is to be subtracted from the first distance.

3 ) Using the same weight draw the mass down an extra 20cm. Once the spring is elongated it is to be let travel. When the spring is released from it? s elongated place the stop watch is started. Once the spring has returned to it? s original get downing place 25 times the timer is to be stopped and the clip is recorded. Once two times are taken for every weight increase they are to be averaged together.

4 ) Stairss 2 and 3 are to be repeated eight times utilizing a new weight each clip.

5 ) When all eight tests are done the spring is to be weighed and recorded.

SAMPLE CALCULATIONS

Mass used in each test, in kgs:

– 50 g / 1000 g = 0.05 kilogram

Elongation of the laden spring, in metres:

– 18.5 / 100 centimeter = 0.185 m

Calculation of ten:

– 22.6 centimeter / 100 centimeter = 0.226 m

– ten = 0.226 m? 0.185 m

– ten = 0.041 m

Calculation for the theoretical value of spring invariable? K:

– K = m g / ten

– K = ( 0.05 kilogram ) ( 9.8 m/s ) / 0.041 m

– K = 12.0 N/m

Calculation for the mean value of the theoretical values of? K? :

– kavg = k1 + k2 + k3 + k4 + k5 + k6 + k7 + k8

8

– kavg = 12.0 + 10.9 + 10.2 + 9.95 + 10.2 + 9.95 + 10.2 + 9.90 + 9.89 + 9.80

8

– kavg = 10.4 N/m

Calculation for the mean clip? T? :

– tavg = t1 + t2

2 & lt ;

/p >

– tavg = 16.5 + 17.2

2

– tavg = 16.9 s

Calculation of the period? T? for one revolution:

– Thymine = T / 25

– Thymine = 16.9 / 25

– Thymine = 0.676 s

Calculation of? T2? :

– T2 = ( 0.676 ) 2

– T2 = 0.457 s2

Calculation for the experimental value of the spring invariable? K? when incline of graph = 4.05:

– K = 4P2 / incline

– K = 4P2 / 4.05

– K = 9.75 N/m

Calculation of? degree Fahrenheits? when: & # 8211 ; y-intercept ( B ) of graph = 0.261

& # 8211 ; mass of spring, MS = 0.173 kilogram

– degree Fahrenheit = K b / 4P2 MS

– degree Fahrenheit = ( 9.75 ) ( 0.261 ) / 4P2 ( 0.173 kilogram )

– degree Fahrenheit = 0.373

Consequence:

Average theoretical value of? K? : K = 10.4 N/m

Experimental value for? K? : K = 9.75 N/m

Mistake:

Average theoretical value of? K? : K = 10.4 N/m

Experimental value for? K? : K = 9.75 N/m

– Actual Error = ( Theoretical Value? Experimental Value ) x 100 %

Theoretical Value

– Actual Error = ( 10.4 ) ? ( 9.75 ) x 100 %

10.4

-Actual Error = 6.25 %

REASONS FOR ERROR

There are many possible grounds for mistake in this lab. Once such ground is that the instrument used are non precision instruments. For case if the metre stick wasn? t absolutely level a measuring which is non accurate would be used in ciphering the Theoretical Value of? K? . If the stop watch wasn? T used decently or stopped or started harmonizing to the processs the clip used will straight impact the consequence of the Experimental Value for? K? therefore making an inaccurate value for? K? . The old mentioned beginnings of mistake can to a certain extent be controlled. However, those beginnings of mistake that can non be controlled are holding no clash and holding zero air opposition.

Decision

Sing all the possible beginnings of mistake, this lab proved to be instead successful. It is evident with mention to the comparatively low Actual Error of 6.25 % .

In holding such a low mistake this concludes that one can happen the spring invariable either dynamically or with Hooke? s Law.