Find the Time Period [ block-spring simple system]

[shivam01anand]

Homework Statement

https://docs.google.com/gview?url=http%3A%2F%2Fwww.mycollegebag.in%2Fuploads%2F9%2F2%2F0%2F3%2F9203182%2Fchapter_12_simple_harmonic_motion.pdf&docid=31dfd636644a39577f33426fb9afdf23&a=bi&pagenumber=6&w=561

Homework Statement

I am referring to the second figure( q19)

It says

"A particle of mass is attached to three springs a,b and c . The blog is compressed towards C( the bottom left one) by a small distance. Find the time period of the subsequent SHM motion.

Homework Equations

The Attempt at a Solution

Okay i tried displacing it towards c by x and the A/B springs by y making an angle θ in the new compressed position.

However I am not sure how to eliminate this y or proceed further.

Moreover if the question was q.20 where all the three springs are symmetrically arranged i was able to just calculate k effective via series parallel as 2/3 * k which gave me the correct answer[is this right first of all?] how can i hope to apply this with the q.19 where angles are not so symmetrical

 

[Simon Bridge]

I don't see any labels on the figures -
The second from the bottom is the only diagram on that page with a spring labelled "C", but it has no "XL" on it so I cannot tell for sure that this is what is intended.

You have sketched the displaced position ... have you resolved all the spring forces into components along (and perpendicular to) the direction of the displacement?

 

[haruspex]

Okay i tried displacing it towards c by x and the A/B springs by y making an angle θ in the new compressed position.

I'm not sure what you mean by y and θ here. Remember that x is taken to be small, so you can approximate the change in length of each of the other two springs as a simple multiple of x. Just consider what component the distance vector x has parallel to spring A.