Resonant frequency of this pendulum?

[unscientific]

Hi everyone,

I'm planning a simple experiment for my school, which involves fixing a mass M onto a rod of length L made of a copper alloy.

Suppose I drive it capacitively, how do I find the resonant frequency of this simple oscillator? I need its resonant frequency to be about 400-500Hz, which would depend on it's geometry.

I know its:

-modulus of elasticity
-density
-Shear modulus
-torsion constant

I have found that the force varies on sin²(ωt), so the drive frequency of the oscillator is the drive frequency of the voltage. I know that at resonance, the amplitude is approxiamtely

≈ Q(τ/k)

but what I need to find is its resonant frequency.

 

[mfb]

There is a formula for the required force to bend a beam with a certain height (here: width) and length by a certain amount. That will look like a spring constant, so you can solve it similar to a spring pendulum.

 

[unscientific]

There is a formula for the required force to bend a beam with a certain height (here: width) and length by a certain amount. That will look like a spring constant, so you can solve it similar to a spring pendulum.

I see, do you know where I can look up an explanation of the formula?

 

[mfb]

Google -> beam bending -> first hit?

 

[PJC01]

I would first like to commend you on planning a simple experiment to explore the resonant frequency of a pendulum. This is a great way to learn about the relationship between the physical properties of a system and its behavior.

To find the resonant frequency of your pendulum, you will need to use the equations for simple harmonic motion and apply them to your specific system. The resonant frequency of a pendulum is dependent on its length, mass, and the force acting on it. In this case, the force is being driven capacitively, so you will also need to consider the electrical properties of the system.

One approach you can take is to use the equation for the period of a simple pendulum, which is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. However, since your pendulum is being driven capacitively, you will also need to consider the electrical properties of the system, such as the capacitance and voltage.

Another approach is to use the equations for the resonant frequency of a driven oscillatory system, which takes into account the driving force and the natural frequency of the system. The natural frequency of your pendulum can be calculated using the equation ω = √(k/m), where k is the torsion constant and m is the mass of the pendulum.

In order to accurately determine the resonant frequency of your pendulum, you will need to measure the physical properties of the system, such as the length, mass, and torsion constant, and also the electrical properties, such as the capacitance and voltage. Once you have these values, you can use the appropriate equations to calculate the resonant frequency.

I hope this helps guide you in your experiment. Remember to always carefully consider the physical and electrical properties of your system and use the appropriate equations to determine the resonant frequency. Good luck with your experiment!