How Do You Calculate the Spring Constant in a Coupled Pendulum System?

[mewmew]

I am given a set up with two pendulums of unknown mass m, of length =.4 meters. They are connected together with a spring of unknown spring constant k. It says when one of the bobs if fixed in place the other has a period of 1.25 seconds. I am then asked to find the period of each normal mode when both bobs are free. I know I need to find k but don't understand how using the information given about the pendulum with a spring attached. I know the frequency of the pinned system but am not sure how to get k from that, as it isn't just equal to k/m.

 

[Gokul43201]

Take the movable bob and displace it by some small distance dx from its equilibrium position. Now what is the total restoring force on it (from gravity + spring) ?