Setting Up DE for Spring Mass Motion

• Benny
In summary, the conversation is about setting up the necessary equations for a physics problem involving a mass attached to a spring. The problem involves determining the equation of motion, downward extension of the spring, and amplitude and period of the motion. The equation of motion is derived using the formula F = m\ddot {x} and the substitution of forces acting on the body. The individual asking for help is a weak physics student and may need more time to understand the problem.
Benny
Can someone help me set up the DE needed for the following problem, there are other similar ones in my booklet so any help with this one should be helpful for the other questions.

Q. A mass of 100kg is attached to a spring suspended from the ceiling of a room, causing the spring to stretch 20 cm upon coming to rest at equilibrium. The spring is then pulled down 5 cm below the equilibrium point and released. Assuming there is no damping and that no external forces are present, determine the equation of motion of the mass and express the downward extension of the spring, x m, from the equilibrium position as a function of time sec., which has elapsed since the mass was released. Also determine the amplitude and period of the motion.

I really only need help with setting up the equation of motion. I haven't seen problems of this type before so I'd like some help. Any pointers would also be good, thanks.

Well, here's how to start. $\vec{F}=m\vec{a}$ This is basically a 1-dimentional problem so rather than a position vector, a single variable x will denote the displacement from equilibrium. Then this equation becomes $F = m\ddot {x}$ Now you need to make a substitution for F in terms of x and you will have a differential equation. The substition will be the forces acting on the body. What forces are these?

Thanks for the help. I'll need to think about the wording of the question a bit more before I can determine an expression for F.

PS: I'm a very weak physics student so it'll probably take me a while.

Last edited:

1. What is "DE" in the context of setting up spring mass motion?

"DE" stands for "differential equation". Differential equations are mathematical equations that describe how a system changes over time. In the context of setting up spring mass motion, DEs are used to model the dynamics of the spring and mass system.

2. What are the key components needed to set up DE for spring mass motion?

The key components needed to set up DE for spring mass motion are the initial conditions (such as the position and velocity of the mass), the parameters of the system (such as the spring constant and mass), and the differential equation that describes the motion of the system.

3. How do I determine the initial conditions for my spring mass system?

The initial conditions for a spring mass system can be determined by measuring the position and velocity of the mass at a specific point in time. These values can also be calculated using equations of motion and the known parameters of the system.

4. What is the role of the differential equation in setting up spring mass motion?

The differential equation is the mathematical representation of the motion of the spring mass system. It takes into account the initial conditions and parameters of the system and describes how the system changes over time.

5. Are there any software or tools that can help with setting up DE for spring mass motion?

Yes, there are many software and tools available that can help with setting up DE for spring mass motion. Some popular options include MATLAB, Wolfram Mathematica, and Python libraries such as SciPy. These tools provide built-in functions for solving DEs and can also plot the results of the simulation.

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