Question 62973
If p denotes the period, l the length and K the constant of proportionality then,

p = K*l^2

When l = 6 ft and p = 2 seconds then,

2 = K*(6^2)

==> 2 = K* 36
==> 2/36 = K*36/36
==> 1/18 = K

Thus the equation becomes p = (1/18)*l^2
when p = 1,

1 = (1/18) l^2
multiplying both the sides by 18,
1*18 = l^2
==> 18 = l^2
taking square root on both the sides,

sqrt(18) = l
==> 4.2 = l

Thus to achieve a period of 1 second, the length should be (approx) 4.2 ft.


Good Luck1!!