- #1

aragorn77777

- 2

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I've been playing around with the following system for the last little while:

(attached image: 2 Blocks + Spring.jpg)

- Block B starts with an initial velocity of 10m/s

I solved the differential equations with a variety of methods in Excel and Mathcad:

Euler

Euler-Cramer

Runge-Kutta (2nd Order)

Adams/BDF

Stiff

Adaptive

Radau

(various options with ODESOLVE)

- All of the methods are in agreement during the first part of the response.

- But there seems to be disagreement in the long term. According to almost all of the solvers, the oscillations continue indefinitely. The stiff solver, however, shows the oscillations eventually settling (relative motion between the two blocks goes to zero and the entire system continues to accelerate to infinity in the direction of the greater force).

1. So the big question is: Will this system ever settle?!

2. A related scenario. If you have:

-mass on a spring with one end fixed

-no damping

-constant external force

Does this system eventually settle? I'd be happy just with a conceptual answer (i.e. - this type of system will never settle down without damping - or - you shouldn't use the Stiff solver if the system is not even close to stiff --- something along those lines) --- I don't expect anyone to sort through the Mathcad solution and come up with numerical answers.

I've attached two Mathcad files:

1. The short term behaviour

2. The long term behaviour (solver set to Stiff)

Any help would be greatly appreciated!

(attached image: 2 Blocks + Spring.jpg)

- Block B starts with an initial velocity of 10m/s

I solved the differential equations with a variety of methods in Excel and Mathcad:

**Excel:**Euler

Euler-Cramer

Runge-Kutta (2nd Order)

**Mathcad:**Adams/BDF

Stiff

Adaptive

Radau

(various options with ODESOLVE)

- All of the methods are in agreement during the first part of the response.

- But there seems to be disagreement in the long term. According to almost all of the solvers, the oscillations continue indefinitely. The stiff solver, however, shows the oscillations eventually settling (relative motion between the two blocks goes to zero and the entire system continues to accelerate to infinity in the direction of the greater force).

1. So the big question is: Will this system ever settle?!

2. A related scenario. If you have:

-mass on a spring with one end fixed

-no damping

-constant external force

Does this system eventually settle? I'd be happy just with a conceptual answer (i.e. - this type of system will never settle down without damping - or - you shouldn't use the Stiff solver if the system is not even close to stiff --- something along those lines) --- I don't expect anyone to sort through the Mathcad solution and come up with numerical answers.

I've attached two Mathcad files:

1. The short term behaviour

2. The long term behaviour (solver set to Stiff)

Any help would be greatly appreciated!