# If a spring is cut in half, does the period change?

by clairez93
Tags: period, spring
 P: 114 1. The problem statement, all variables and given/known data A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. Particle oscillates as shown in (i) with preriod T. If the spring is cut in half and used with the same particle, as shown in (ii), the period will be. A) 2T B) $$\sqrt{2}$$T C) T/$$\sqrt{2}$$ D) T E) T/2 2. Relevant equations T = 2$$\pi$$$$\sqrt{m/k}$$ 3. The attempt at a solution I figured that since the length of the spring isn't relevant to the period, the period would stay the same. The answer provided is C. I'm not sure why. Attached Thumbnails
 P: 114 Oh I see. So the first spring: $$k = mg/x$$ Thus, $$T = 2\pi\sqrt{x/g}$$ So in the second spring: $$k = 2mg/x$$ Thus, $$T' = 2\pi\sqrt{x/2g} = T/\sqrt{2}$$ Is this correct?