Question 83017
The period (T) of a simple pendulum is directly proportional to the square root of its length (L).  If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shorten to achieve a 1 second period? The answer is multiple choice.

a. 1 foot
{{{highlight(b)}}}. 1.5 feet
c. 2 feet
d. 3 feet
Directly proportional means multiply, k is the proportionality constant:
{{{T=k*sqrt(L)}}}, L=6 and T=2, find k
{{{2=k*sqrt(6)}}}
{{{2/sqrt(6)=k}}}
The formula is 
{{{T=(2/sqrt(6))*sqrt(L)}}} let T=1 and find L
{{{1=(2/sqrt(6))*sqrt(L)}}}
{{{(sqrt(6)/2)*1=(sqrt(6)/2)(2/sqrt(6))*sqrt(L)}}}
{{{sqrt(6)/2=sqrt(L)}}}
{{{(sqrt(6)/2)^2=(sqrt(L))^2}}}
{{{6/4=L}}}
{{{3/2=L}}}
L=1.5 feet