How long must a simple pendulum be if it is to make exactly one swing per second? (That is, one complete oscillation takes exactly 2.0 s.)
In order to watch this solution you need to have a subscription.
This is Giancoli Answers with Mr. Dychko. Period of the pendulum is 2π times the square root of its length divided by acceleration due to gravity and you can divide both sides by 2π and switch the sides around and have square root l over g is T over 2π square both sides and you get l over g is T squared over 4π squared and then multiply both sides by g and you get l is the length of the pendulum is period squared times g over 4π squared so, the period we're told is actually 2 seconds. So, one complete oscillation is the time we're looking for, 2 seconds there. And we square that, times 9.8 meters per second squared divided by 4π squared and that's 0.99 meters would be the required length.
Is this calculation correct? It shows 4/pi^2 on the calculator display.
Hi donnarrnc,
Thanks for the question. Yes, things are all good here. The calculator display shows /4/pi^2, which is another way of saying what you might have been expecting: /(4pi^2).
All the best,
Mr. Dychko
Find us on:
