# Ruler Resonance frequency equation?

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#1
How can I model a ruler so I can find a relationship between its resonance frequency and length?
0
1 year ago
#2
(Original post by rohanjain2602)
How can I model a ruler so I can find a relationship between its resonance frequency and length?
If you twang a ruler with your finger when the ruler is fixed at the edge, the vertical oscillation height will follow a Damped Simple Harmonic Motion solution of a second order differential equation.
As a start
Use different overhang lengths..... record the period and the number oscillations it took for the displacement to return to zero:
If possible, record the displacement after each oscillation (*difficult without a video production in operation)

If you want to simplify the process, forget damping ..record just length and period for each overhang length.
The period should be measued by timing the a number of oscillations over a time, then finding the time for one oscillation .
Then frequency is 1/period
Tabulate values of frequency (yaxis) F .........against length (x axis ) ..L

Draw THREE separate graphs
Plot F against L
Plot Log F against Log L
Plot Log F against L

See which graph fits the best ..then do the Maths
Last edited by swinroy; 1 year ago
0
#3
(Original post by swinroy)
If you twang a ruler with your finger when the ruler is fixed at the edge, the vertical oscillation height will follow a Damped Simple Harmonic Motion solution of a second order differential equation.
As a start
Use different overhang lengths..... record the period and the number oscillations it took for the displacement to return to zero:
If possible, record the displacement after each oscillation (*difficult without a video production in operation)

If you want to simplify the process, forget damping ..record just length and period for each overhang length.
The period should be measued by timing the a number of oscillations over a time, then finding the time for one oscillation .
Then frequency is 1/period
Tabulate values of frequency (yaxis) F .........against length (x axis ) ..L

Draw THREE separate graphs
Plot F against L
Plot Log F against Log L
Plot Log F against L

See which graph fits the best ..then do the Maths
kk but can this be modelled as a closed tube standing wave system or something? Is there any given equation for resonance with respect to height. Currently im seeing a straight line for this graph i plot for resonance frequency by height → 1/F^(0.5) = H . Is there something to explain this?
0
1 year ago
#4
(Original post by rohanjain2602)
kk but can this be modelled as a closed tube standing wave system or something? Is there any given equation for resonance with respect to height. Currently im seeing a straight line for this graph i plot for resonance frequency by height → 1/F^(0.5) = H . Is there something to explain this?
To explain the relation you need to look at the definition of SHM and state that
Acceleration = - omega squared times x
In other words you need to equate the restoring force to mass x Acceleration
Easy for a spring but difficult for a ruler. I have never done that
There was a further maths exam question in 2019 core pure 2 that was exactly your set up except it was a diver on a diving board who launched himself off it and caused the board to execute DAMPED SHM
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