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## Homework Statement

a mass m hangs from a uniform spring of spring constant k.

(a)what is the period of oscillations in the system?

(b)what would it be if the mass m were hung so that:

1)it was attached to two identical springs hanging side by side?

2)it was attached to the lower of two identical springs connected end to end?

(P.S. Im not sure if we are to neglect the force of weight of the mass)

## Homework Equations

[itex]T=2\pi /\omega [/itex]

## The Attempt at a Solution

**(a)**[itex]m\ddot{x} +kx=0[/itex]

dividing by "m" you get: [itex]\ddot{x}+\omega^2 x=0[/itex]

to find the roots: [itex]r^2 +\omega^2 = 0[/itex]

to which the roots are: [itex]r=\pm i\omega[/itex]. According to this equation the angular frequency is [itex]\omega[/itex] which equals [itex]\sqrt{k/m}[/itex].

Therefore, [itex]T=2\pi \sqrt{m/k}[/itex]

**(b)(1)**skipping a few steps because its similar to last equation you get [itex]\ddot{x} +\omega^2 x=0[/itex]

again finding the roots you get: [itex]\pm \omega \sqrt{2} i [/itex],

According to this equation the angular frequency is [itex]\sqrt{2}\omega[/itex] which equals [itex]\sqrt{2k/m}[/itex].

the period is: [itex]2\pi \sqrt{m/2k}[/itex]

**(b)(2)**im not really sure how to set this one up but my thinking was something like this.

I can write the spring force as if it were 1 spring of length 2L.

but the thing is that the oscillations dont depend on the length of the spring, and im not sure if this is a correct way of going about it. Please help.