How Period of Two Simple Harmonic Oscillators Differ with Diverse Parameters - Lab Report Example

The application of these experiments is immensely in the fabrication sectors where engineers construct diverse models to come up with refined designs meant to construct real machines and objects. Graphs This section features two graphs; Weight vs. Extension Graph (F = kx)Length of the string used (m) vs. PeriodSimple Harmonic experimentObjective: The aim of this experiment was to ascertain how the period of two Simple Harmonic oscillators (pendulum and spring-mass system) differ with diverse parameters.

Apparatus Simple pendulum Supporting rod, clamp, hook for suspending spring and short rod2 M stick with Vernier caliper jawsCylindrical spring type weights (100g, 200g, 300g, 500g) Stopwatch or stop clockTriple beam balance method Procedure Pendulum experiment The first step was to measure the diameter of the metal sphere (2.5cm) and hanging it from support with a string of length 0.6m before displacing it at an angle of 50. Then the timing of 50 oscillations followed together with the recording of the attained results.

The second step entailed repetition of the initial step but with varying lengths (0.8m, 1.0m, 1.2m, 1.4m, and 1.6m) coupled with recording oscillations after every 25 vibrations instead of 50 as it was in the first procedure. Using a 0.5m length string and tilted at diverse angles (00, 300, and 450) for 50 oscillations, results were tabulated in the table. Spring mass experiment This experiment entailed hanging the spring instead of string from the support with varying masses at its base (0.1kg, 0.2kg, 0.3kg, 0.4kg, and 0.5kg). Then displacing each mass in turn from their middle positions, measuring their displacements, and tabulating them in a table.

Results Diameter of the sphere = 2.55 cm Radius of the sphere = 1.275 cmTable 1: Pendulum statisticsLength of the string used (cm)Length of the string used (m)Length of the pendulum. of vibrationsTimePeriodSquare of period58.70.587605077.5451.5512.40578.70.787805089.341.7873.19398.70.9871005099.651.9933.972118.71.1871202555.142.2064.864138.71.3871402559.82.3925.722158.71.5871602563.272.5316.406Value of g from the slope = 9.7w/s Percent error Normal earth’s pull = 9.8w/sThen, % deviation = (9.8-9.7)/9.

8 = 1.02Length of the string used = 48.7 cm Length of pendulum = 51.2 (48.7 + 2.5)Table 2: Pendulum statisticsInitial displacement of sphere number of vibrationsTimePeriodSquare of period505071.141.4222.0243005071.871.4372.0664505073.611.4722.167Per 0.25g, Converting to Newtons multiply by 9.81, Free extension = 6.47 cm. Table 3: Spring statisticsMass suspended from the spring (Kg)Weight (N)Force stretching spring (g)Scale readingElongation (cm)0006.4700.10.98110010.283.810.21.962200147.530.32.94330017.9511.480.43.92440021.815.330.54.90550025.4518.98Mass of the spring = 9g, Force constant of the spring = 3. 914n/mTable 4: Spring ReadingsMass suspended from the spring (kg)Mass of the vibrating system (g)Amplitude of vibration time for 50 vibrationsPeriodPercent discrepancyExperimental value calculated value0.2209528.290.1351.64111.20.22091028.680.1371.64111.20.5509544.300.0872.59328.8Applications: The application of these experiments is immensely in the fabrication sectors where engineers construct diverse models to come up with refined designs meant to construct real machines and objects. This is to minimize losses, which could have occurred if the specialists ignored small tests in determining how the real design will work.