Frequency help?
Tarzan swings back and forth on a long vine. His friend Jane notices 30.swings in 2.4 minutes what is the frequency and what is the vine length?
I got the frequency at .208Hz which when I converted it to T (f=1/T) I got 4.81 then I plugged it into my equation T=2(pi)√(L / g)
but I end up getting 557 as my answer which does not seem right. Can you tell me where I went wrong?
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Verified answer
Frequency is cycles per second, so:
f = 30 / (2.4 minutes * 60 seconds / minute) = 0.208 Hz, as you found
Period is seconds per cycle or the inverse of frequency:
T = 1/f = 1 / 0.208 Hz = 4.8 seconds
As you wrote, period of a simple pendulum is:
T = 2π√(L/g)
Substituting:
4.8 s = 2π√(L/9.8 m/s²)
0.764 s = √(L/9.8 m/s²)
0.584 s² = L / 9.8 m/s²
5.72 m = L
The vine is 5.72 meters long.
Not sure where you made your mistake. Typo in your calculator somewhere?