# Simple Harmonic Motion

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OBJECT:

The objective of this lab is to obtain the spring constant by using the simple harmonic motion of the spring-mass system. Once the spring constant is obtained it is to be compared to the spring constant obtained by Hooke's Law.

PROCEDURE:

1) Using a meter stick measure the distance from the attached point of the spring to the end of the spring, at this time there is to be no mass on the spring. Once this measurement is obtained the elongations can be calculated by subtracting the new measurements from this first measurement.

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 pull the mass down an additional 20cm. Once the spring is elongated it is to be let go. When the spring is released from it's elongated position the stopwatch is started. Once the spring has returned to it's original starting position 25 times the timer is to be stopped and the time is recorded. Once two times are taken for every weight increment they are to be averaged together.

4) Steps 2 and 3 are to be repeated eight times using a new weight each time.

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

SAMPLE CALCULATIONS

Mass used in each trial, in kilograms:

- 50 g / 1000 g = 0.05 kg

Elongation of the loaded spring, in meters:

- 18.5 / 100 cm = 0.185 m

Calculation of x:

- 22.6 cm / 100 cm = 0.226 m

- x = 0.226 m Ð'- 0.185 m

- x = 0.041 m

Calculation for the theoretical value of spring constant "k:

- k = m g / x

- k = (0.05 kg) (9.8 m/s) / 0.041 m

- k = 12.0 N/m

Calculation for the average 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 average time "t":

- tavg = t1 + t2

2

- tavg = 16.5 + 17.2

2

- tavg = 16.9 s

Calculation of the period "T" for one revolution:

- T = t / 25

- T = 16.9 / 25

- T = 0.676 s

Calculation of "T2":

- T2 = (0.676)2

- T2 = 0.457 s2

Calculation for the experimental value of the spring constant "k" when slope of graph = 4.05:

- k = 4P2 / slope

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