How to do simulate a resonant frequency?

In summary, The question is about predicting the position and amplitude of an object in sinusoidal motion, taking into account a constant force pushing it towards the center point, as well as additional forces and resistance. The end goal is to calculate the amplitude at any given time with varying forces. The issue of adjusting to a change in phase and finding the ideal resistance for a given frequency also needs to be addressed. Resources suggested for further understanding include an ODE book and an undergraduate physics classical mechanics text.
  • #1
inhahe
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Hello, I have a question on how to do something. I'm not sure whether calculus or trigonometry is needed. this is not a homework question.

an object will move left and right of a center point in a sinusoidal motion. the period is always the same; the amplitude should change. at any point in time F=kd, where F is the force pushing the object toward the center point, d is its distance from the center, and k is some constant.

If i have the object's position and velocity relative to center and I push or pull it with a certain force (in addition to F), let's say "G", I need to predict where it will end up after one-half a period. I also need to factor in resistance -- the object will have some amount of resistance to its motion.

The end goal is to do this many times with varying G's and calculate the amplitude at which it's moving back and forth at any particular time. so if position and/or velocity can be forgone completely so that we only arrive at intensity from G inputs that would work too.

come to think of it, if the period is always the same then the thing can't adjust to a change in phase of an input frequency (i'm simulating sympathetic resonance here), so I'm not sure how sympathetic resonance adjusts to changing phase. that has to be accounted for too.

also I need to know the ideal resistance for a given frequency so that the amplitude doesn't add up indefinitely.
 
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  • #2
A standard ODE book would have this. You could look up an undergrad physics classical mechanics text too.
 

FAQ: How to do simulate a resonant frequency?

1. How do you determine the resonant frequency of a system?

To determine the resonant frequency of a system, you can use the formula f = 1/(2π√LC), where f is the resonant frequency, L is the inductance, and C is the capacitance of the system. Alternatively, you can also use a signal generator and an oscilloscope to find the frequency at which the amplitude of the system is at its maximum.

2. What is the significance of a resonant frequency in a system?

A resonant frequency is the frequency at which a system naturally vibrates or oscillates at its maximum amplitude. It is an important characteristic of a system as it can affect its stability and performance. It is also useful in applications such as tuning musical instruments and designing electrical circuits.

3. How can you simulate a resonant frequency in a laboratory setting?

To simulate a resonant frequency in a laboratory setting, you can use a signal generator and an oscilloscope to generate and measure the frequency at which the system reaches its maximum amplitude. You can also use mathematical equations to calculate the resonant frequency based on the properties of the system, such as inductance and capacitance.

4. What factors can affect the resonant frequency of a system?

The resonant frequency of a system can be affected by various factors such as the physical properties of the system, including its mass, stiffness, and damping. The type and placement of external forces can also affect the resonant frequency. Additionally, changes in the system's temperature or environment can alter its resonant frequency.

5. How can you manipulate the resonant frequency of a system?

The resonant frequency of a system can be manipulated by changing its physical properties, such as its mass or stiffness, or by altering the external forces acting on it. In electrical systems, the resonant frequency can be adjusted by changing the values of inductance and capacitance. Additionally, adding dampers or using active control techniques can also modify the resonant frequency of a system.

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