How Does Doubling the Springs Affect the Oscillation Period?

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Homework Help Overview

The discussion revolves around the effect of doubling springs on the oscillation period of a mass-spring system. The original poster describes a setup with two identical springs attached to a mass and seeks to understand how this configuration influences the period of oscillation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the formula for the period of oscillation, questioning how to modify the spring constant when two identical springs are involved. Participants explore the total force exerted by the springs and its implications for the period calculation.

Discussion Status

Participants have engaged in clarifying the relationship between the forces exerted by the two springs and the resulting equation for the period. There is a shared understanding of the force expression, and a potential formula for the period has been suggested, though no consensus on the final outcome has been reached.

Contextual Notes

Participants are working within the constraints of a homework problem, focusing on the theoretical implications of spring constants and their effect on oscillation periods without providing a definitive solution.

map7s
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There is a spring with one end attached to a wall and the other end attached to a mass of 1.19 kg. On the other side of the mass is another spring whose other end is attached to another wall. The springs are identical and have a spring constant value of 49.7 N/m. What is the period?

I drew out a picture and I know that I need to use the equation T=2pi*square root of mass/k but with some modifications to the k. At first I thought that, with the spring being identical on both sides, the spring force would cancel out, but obviously that was wrong. How would I be able to use a modified form of this equation to solve for the period?
 
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There might be a simplification that would help. In the linear region, the spring force is just F=kx, where x is the displacement, regardless of whether it is compression or tension. If you displace the block to the right some distance, that is seen by one spring as compression and by the other as tension, right? What is the total force on the block from the 2 springs, expressed in terms of the value k and the displacement?...
 
Would it just be F=2kx ?
 
map7s said:
Would it just be F=2kx ?
Yep. So that simplifies working out the answer for the period, right?
 
So, would I have to use the equation T=2pi*square root of m/(2k) ?
 
map7s said:
So, would I have to use the equation T=2pi*square root of m/(2k) ?
That will do it.
 

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