Amplitude Change in Oscillations with Varying Spring Constants

  • Thread starter Thread starter morrisj753
  • Start date Start date
  • Tags Tags
    Amplitude Spring
Click For Summary

Homework Help Overview

The discussion revolves around a physics problem involving oscillations of a mass attached to springs with different spring constants. The original poster presents a scenario where a mass oscillates with a certain amplitude when attached to a spring of constant k, and then questions how the amplitude changes when the spring constant is doubled to 2k while maintaining the same initial velocity.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of energy conservation equations to relate the initial velocity and amplitude. There is an exploration of how the change in spring constant affects the amplitude of oscillation. Questions are raised about the relationship between the original amplitude and the new amplitude.

Discussion Status

Participants are actively engaging with the problem, offering insights into the relationships between the variables involved. Some have provided algebraic manipulations to express the new amplitude in terms of the original amplitude, indicating a productive exploration of the topic.

Contextual Notes

The original poster expresses uncertainty about the appropriate equations to use, and there is a focus on deriving relationships rather than reaching a definitive conclusion. The discussion reflects an ongoing examination of the assumptions related to the spring constants and their impact on oscillation amplitude.

morrisj753
Messages
11
Reaction score
0

Homework Statement


A mass is attached to the wall by a spring of constant k. When the spring is at its natural length, the mass is given a certain initial velocity, resulting in oscillations of amplitude A. If the spring is replaced by a spring of constant 2k, and the mass is given the same initial velocity, what is the amplitude of the resulting oscillation?

Homework Equations


E = 1/2mv^2 + 1/2kx^2 = 1/2kA^2

The Attempt at a Solution


I am not quite sure what equation to really apply here, or how to approach the problem to find the amplitude. The answer is 1/(√2).
 
Physics news on Phys.org
The velocity is given when the spring is relaxed. So you get the amplitude from the equation 1/2mv^2 =1/2kA^2

Double the spring constant: k'=2k. Now you have the equation for the new amplitude A'. 1/2mv^2 =1/2 k' A'^2 . V is the same, so 1/2kA^2= 1/2 k' A'^2. How are A and A' related?


ehild
 
well, by substituting k' = 2k,
you end up with A^2 = 2 (A')^2
 
Isolate A'.

ehild
 
You end up with 1/√2 A, which is the correct answer.
Thank you very much for the help!
 

Similar threads

Replies
3
Views
988
  • · Replies 1 ·
Replies
1
Views
8K
Replies
3
Views
1K
  • · Replies 29 ·
Replies
29
Views
2K
Replies
29
Views
3K
Replies
5
Views
2K
Replies
17
Views
3K
Replies
1
Views
2K
Replies
9
Views
2K