Spring and Hammer Problem: Calculate Motion w/m, k, J, t

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Homework Help Overview

The discussion revolves around a physics problem involving a mass on a spring, subjected to an impulse. The participants explore the dynamics of the system using concepts from mechanics and differential equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formulation of the motion equation, questioning the appropriateness of using a standard force equation versus incorporating impulse effects through a Dirac delta function. There is also mention of using Laplace Transforms for solving the problem.

Discussion Status

The conversation has progressed with some participants suggesting initial conditions and differential equations based on the impulse applied to the mass. However, there is no explicit consensus on the approach to take, as different methods are being considered.

Contextual Notes

Participants are encouraged to make simplifying assumptions due to the problem's origin from a general physics textbook, which may influence the complexity of the solutions discussed.

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Problem: A mass m is at rest on the end of a spring of spring constant k. At t = 0 it is given an impulse J by a hammer. Write the formula for the subsequent motion in terms of m, k, J, and t.

Would ma = -kx + J/t be an acceptable answer?
 
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No, it is not!
The force associated by impulse J should be modeled by Dirac's delta function; solve the problem with Laplace Transforms.
 
Last edited:
Please note that the problem is from a general physics textbook. Assume as many simplifying assumptions as possible.
 
In that case, solve it as follows:
Just after the impulse J, the mass has an initial velocity [tex]v_{0}=\frac{J}{m}[/tex]
In the subsequent problem, your diffferential equation is:
[tex]-kx=m\ddot{x}[/tex]
whereas initial conditions are:
[tex]x(0)=0,\dot{x}(0)=\frac{J}{m}[/tex]
 
Last edited:
Hmm...Why didn't I think of that? I guess that does it for that problem. Thanks.
 

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