Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion is a type of periodic motion where an object oscillates around an equilibrium position. In this context, the cantilever behaves like a spring-mass system, where the restoring force is proportional to the displacement from the equilibrium. The frequency of oscillation is determined by the mass of the system and the spring constant, which influences how quickly the system can return to equilibrium after being disturbed.
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Frequency and Mass Relationship
The frequency of oscillation in a spring-mass system is inversely related to the square root of the mass. Specifically, the formula for the frequency (f) is given by f = (1/2π)√(k/m), where k is the spring constant and m is the mass. When additional mass is added to the system, such as the DNA molecules in this experiment, the frequency decreases, allowing for the calculation of the mass based on the change in frequency.
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Measurement Precision and Significant Figures
Measurement precision refers to the degree of refinement with which a measurement is made, while significant figures indicate the number of meaningful digits in a number. In this experiment, although the mass and spring constant can only be determined to two significant figures, the oscillation frequency can be measured with high precision. This distinction is crucial for accurately calculating the mass of the DNA from the observed change in frequency.
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