Find when spring oscillates less than X

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In summary, the conversation discusses the use of spring equations to determine when a spring will oscillate with a rate of change less than a certain value, denoted as X. The speaker is unsure of where X fits into the standard equations and the level of physics involved. However, it is suggested that if the damping is linear, the motion will have exponential decay and the solution can be found by setting the rate of change equal to X and solving the equation.
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Acreol
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Given the spring equations in the desmos (pretty sure they are standard from
https://en.wikipedia.org/wiki/Harmonic_oscillator
, but if they aren't please say so), how would you find when the spring will oscillate with a rate of change less than X (I'm using this to determine when the spring is steady)

https://www.desmos.com/calculator/63lncxcjmk

Also I'm not really sure what level of physics this is so if I got it wrong, please let me know ;P
 
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Acreol said:
with a rate of change less than X
I'm not sure what you mean by "X". Where does this fit into the standard equations? If the damping is linear then the motion has exponential decay and the decay graph has the same (scaled) shape for all start amplitudes. Envelope of Amplitude / Rate of change / higher derivatives etc. will all have the exponential form so it looks as if the answer to your question could be "it's easy":smile: Just solve the equation for rate of change = X.
 
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1. What is spring oscillation and why is it important to measure?

Spring oscillation is the back-and-forth motion of a spring when it is stretched or compressed. It is important to measure because it can provide information about the properties of the spring, such as its stiffness or elasticity. This information can be useful in various fields, such as engineering and physics.

2. How do you measure the amount of oscillation in a spring?

The amount of oscillation in a spring can be measured using a variety of methods, such as attaching a weight to the end of the spring and measuring the displacement, or using sensors to track the motion of the spring and calculate the amplitude of oscillation.

3. Can the amount of oscillation in a spring be controlled?

Yes, the amount of oscillation in a spring can be controlled by adjusting the factors that affect its motion, such as the mass attached to it, the initial displacement, and the stiffness of the spring itself.

4. What factors can affect the amount of oscillation in a spring?

The amount of oscillation in a spring can be affected by several factors, including the mass attached to the spring, the initial displacement, the stiffness of the spring, and any external forces acting on the spring.

5. Why is it important to find when spring oscillates less than X?

Finding when a spring oscillates less than a certain value can provide information about the spring's behavior at different levels of displacement. This can be useful in designing and optimizing systems that use springs, such as in shock absorbers or suspension systems.

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