Core Practical 16: Investigating Resonance

Determine the value of an unknown mass by a graphical method by using the resonant frequencies of the oscillation of known masses

Variables

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Set up the spring with 100 g mass attached
On the stand make a clear fiducial mark about 5 cm below the bottom of the spring
Extend the spring so that the bottom is level with the fiducial marker, release and start timing
Measure time for 10 oscillations
Repeat with the same mass two more times
Find the average time period of one oscillation
Add 100 g and adjust the fiducial mark downwards so that it is 5 cm below the new level of the spring
Repeat steps 3-7 until the total mass is 500 g
Plot a graph of T² on the y-axis against m on the x-axis

Follow steps 2 - 6 for the test mass
Find the value of the time period, T and square it to find T²
On the graph mark a horizontal from T² to the graph line and where they intersect, take the arrow vertically down to meet the x-axis
The value of m which this line coincides with is the mass of the test mass
Check the result using digital scales

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$2 π f = \sqrt{\frac{k}{m}}$

$\frac{2 π}{T} = \sqrt{\frac{k}{m}}$

$\frac{4 π^{2}}{T^{2}} = \frac{k}{m}$

$T^{2} = m (\frac{4 π^{2}}{k})$

Plot a graph of T² on the y-axis against m on the x-axis to get a straight line through the origin with;

gradient = $(\frac{4 π^{2}}{k})$

Core Practical 16: Investigating Resonance (Edexcel International A Level Physics)