3 identical masses and four identical springs are set up as shown (m=mass ~=spring |=fixed point)(adsbygoogle = window.adsbygoogle || []).push({});

|~m~m~m~|

the two outside masses are displaced equally inwards. What is the effective spring constant of this system.

attempt at solution:

using FBDs F=-2kx on each individual outside mass

middle mass is stationary at all times, since the two inside springs will cancel each other out, so it acts as if T= 2pi rad(m/2k) (as if it were just |~m~|), but you double the mass for the system (only 2m is moving), but keep the period the same so keff = 4k

i'm not sure how correct this is, or whether the assumptions i made are even correct. This is how a classmate explained it to me, i personally left it as 2k since i couldn't logically justify making it 2m in the period equation since the system didn't follow the standard oscillation I'm used to.

i probably should stic a question here as well, lol

is this correct? It sounds as if I'm missing something, or that using period is the wrong approach to the problem.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Effective Spring Constant

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**