Problem26
Section 16.4: The Simple Pendulum

Question

The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency?

Question by OpenStax is licensed under CC BY 4.0

Final Answer

2.23 Hz2.23\textrm{ Hz}

Solution video

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Video Transcript

This is College Physics Answers with Shaun Dychko. A simple pendulum has a length of 5.00 centimeters which is 5.00 times 10 to the minus 2 meters since the prefix 'centa' means multiply by 10 to the minus 2 and we want to find the frequency of this pendulum. Well we know a formula for its period is 2π times the square root of the length divided by acceleration due to gravity and frequency is the reciprocal of the period—it's 1 over period— and so if we take the reciprocal of this then that will give us the answer for frequency. So that's 1 over 2π times square root of g over L, where I flipped each of the fractions; this 2π is a fraction of 2π over 1 and then taking its reciprocal makes 1 over 2π. So then we have 1 over 2π times square root 9.80 meters per second squared divided by 5.00 times 10 to the minus 2 meters and that is 2.23 hertz. So this pendulum will swing a complete swing starting from its beginning point and back to its beginning point 2.23 times every second.

Comments

bmudge·
Could you please explain why on the calculator you did 1/2/pi, when the equation is written as 1/2*pi? I did the problem correctly but my answer was off by a factor of 10 and I'm confused as to where/why the conversion happens. Thank you!!
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ShaunDychko·
Hi bmudge, thank you for the question. I can't really guess why your answer is off by a factor of 10, but I can explain 1/2/pi. 1/2/pi is the same as 1/(2\*pi). The calculator evaluates division left to right, so it evaluates 1/2 first, then divides that answer by "pi", which is equivalent to 1/(2\*pi), but 1/2/pi has less calculator button pushing since there's no need to type in the brackets. It's just a personal preference. Keep in mind that 1/2\*pi, however, is **not** the same, since that would mean "divide one by 2, and multiply that answer by pi", since there are no brackets to package the factors 2 and pi in the denominator. Hope this helps, Shaun
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bmudge·
Thank you!
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