Max Amplitude for a 2 mass oscillation system

[daredevile125]

Homework Statement

A mass of "m" is attached to the bottom of a vertical suspended spring with spring constant "k". Attached to that mass is a string , that is connected to a second mass also equal to "m".

What is the maximum amplitude for the two-mass oscillation system in order for it to remain "simple harmonic" ?

 

[Spinnor]

As the amplitude increases the acceleration of the masses increases. When the acceleration is greater then that of gravity there will be slack in the string?

 

[daredevile125]

ahh thank you that sounds reasonable, I was thinking it had something to do with the spring being inelastic anymore , but that makes more sense , tyvm.

 

[daredevile125]

acc max = A w^2

g = A K/2m

A= 2gm/k

 

[asteriatic]

I would first clarify that the term "simple harmonic" refers to a type of motion where the restoring force is directly proportional to the displacement from equilibrium and the motion is periodic. In this case, the system described above can be considered a simple harmonic oscillator if the masses are small and the displacement is small compared to the length of the spring.

To determine the maximum amplitude for this system, we can use the equation for simple harmonic motion, which is A = F/K, where A is the amplitude, F is the restoring force, and K is the spring constant. In this case, the restoring force is equal to the weight of the masses, which can be calculated as mg, where g is the acceleration due to gravity.

Therefore, the maximum amplitude for this system can be calculated as A = mg/K. This means that the maximum amplitude is directly proportional to the mass and inversely proportional to the spring constant. In other words, a larger mass or a smaller spring constant will result in a larger maximum amplitude.

It is important to note that this calculation assumes ideal conditions and does not take into account any external factors such as air resistance or friction. These factors can affect the maximum amplitude of the system and may need to be considered in a more complex analysis. Additionally, the maximum amplitude calculated here is for a system that is in simple harmonic motion. If the system experiences damping or other non-ideal behaviors, the maximum amplitude may be different.

In conclusion, the maximum amplitude for a two-mass oscillation system to remain in simple harmonic motion can be calculated using the equation A = mg/K, where A is the amplitude, m is the mass of the objects, g is the acceleration due to gravity, and K is the spring constant. This calculation provides a basic understanding of the system and can be used as a starting point for further analysis.