A mass attached to two springs with different k values

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A mass attached to two springs with different spring constants (k1 and k2) experiences a total restoring force calculated as F = -k1x - k2x, leading to an effective spring constant of k = k1 + k2. This indicates that the springs behave as if they are in parallel, not in series. The discussion highlights the importance of understanding the configuration of springs when analyzing their combined effects on frequency and force. Further exploration of the scenario where the springs are connected in series is suggested for a deeper understanding. The initial analysis regarding the combined k values is confirmed as correct.
darrenhb
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Hey. Suppose a mass is attached to two springs, one on each side, and they have different values for k. If you wanted to measure the frequency, how would you add up the k values? Would it work as if they were in series, so 1/k = 1/k1 + 1/k2, or would it just be k = k1 + k2 like in parallel? Or something else?

Thanks!
 
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See if you can figure it out. Imagine the mass pushed a distance X from equilibrium. What's the total restoring force from the two springs?
 
What I figured was that it would be F = -k1x - k2x, and therefore k = k1 + k2. Is this correct?

I always over-think these things!
 
darrenhb said:
What I figured was that it would be F = -k1x - k2x, and therefore k = k1 + k2. Is this correct?
You got it. :approve:

(Now you should figure out how things would be different if the springs were connected together in series.)
 
Thanks! I'll give that a go later, haha.
 

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