# word problem

• Jun 29th 2006, 10:14 AM
kwtolley
word problem
The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what lemgth should it be shortened to achieve a 1 second period? My answer is 3 feet but I'm not sure. Thanks for checking this problem.
• Jun 29th 2006, 02:49 PM
CaptainBlack
Quote:

Originally Posted by kwtolley
The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what lemgth should it be shortened to achieve a 1 second period? My answer is 3 feet but I'm not sure. Thanks for checking this problem.

What we are told may be rewritten as:

$period(length)=k\sqrt{length}$

also:

$period(6)=k\sqrt{6}=2$

so: $k=2/ \sqrt{6}$

Now if the period is 1 s:

$period(length)=2/ \sqrt{6}\times \sqrt{length}=1$

rewriting this gives:

$length=3/2\ ft$

RonL
• Jul 3rd 2006, 11:09 AM
kwtolley
Ok I see your answer but I have to chose 1 foot, 1.5 feet, 2 feet, or 3 feet. I guess it is 1.5 feet. thanks for all the help given.
• Jul 3rd 2006, 01:09 PM
CaptainBlack
Quote:

Originally Posted by kwtolley
Ok I see your answer but I have to chose 1 foot, 1.5 feet, 2 feet, or 3 feet. I guess it is 1.5 feet. thanks for all the help given.

I think you will find that 3/2=1.5 ft, so yes.

RonL
• Jul 4th 2006, 01:40 AM
kwtolley