A Pendulum That Ticks Seconds

Q. Taking g as 9.8 m/s², what is the length of a simple pendulum, which ticks seconds, in metres? expects 0.99 m

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The web of concepts

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The equations it used

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Q. Taking g as 9.8 m/s² $g_{e} = 9.8$ m/s², what is the length of a simple pendulum, which ticks seconds $T_{p} = 2$ s, in metres?

The playground

Inputs

gravity

g_{e}

9.8 m/s²

Outputs

length

L_{p}

The solution

Solved with SimplePendulum

Given

$g_{e} = 9.8$ m/s²
$T_{p} = 2$ s from “ticks seconds”

Find $L_{p}$ .

Working

period of a simple pendulum(pendulum) $T_{p} = 2 \cdot π \cdot \sqrt{\frac{L_{p}}{g_{e}}}$
$2 = 2 \cdot 3.14159265 \cdot \sqrt{\frac{L_{p}}{9.8}}$
$L_{p} = 0.99 m$
$L_{p} \approx 0.99$ mto 2 significant figures

Conclusion

A pendulum that ticks once a second swings there and back in two, and that period fixes its length: about a metre.

The Ruby

1require_relative "../physics"23question :a_pendulum_that_ticks_seconds do4  kind :numerical5  describes "Taking g as %{gravity}, %{length}, in metres?"6  given gravity: "9.8 m/s2"7  asks length: "what is the length of a simple pendulum, which ticks seconds"8end

1require_relative "../questions/a_pendulum_that_ticks_seconds"2require_relative "../science/oscillations/simple_pendulum"34solve :a_pendulum_that_ticks_seconds, using: SimplePendulum do5  objects :earth6  object :pendulum, on: earth78  take gravity: earth.surface_gravity910  deduce_from "ticks seconds", pendulum.period => "2 s"1112  length = pendulum.length_of_the_string13  answer length:, in: "m", figures: 21415  conclusion "A pendulum that ticks once a second swings there and back in two, and that period fixes " \16             "its length: about a metre."17end

1require_relative "../solutions/a_pendulum_that_ticks_seconds"23play_with :a_pendulum_that_ticks_seconds do4  title "A Pendulum That Ticks Seconds"5end

The laws

quantity	written	units	within	from
pi	$π$	—	0 … ∞	SimplePendulum
surface gravity	$g$	m/s²	—	SimplePendulum
length of the string	$L$	m	—	SimplePendulum
period	$T$	s	—	SimplePendulum
period of pendulum	$T_{p}$	s	—
length of the string of pendulum	$L_{p}$	m	—
surface gravity of earth	$g_{e}$	m/s²	—
length of the string of earth	$L_{e}$	m	—
period of earth	$T_{e}$	s	—
surface gravity of pendulum	$g_{p}$	m/s²	—

T_{b} = 2 \cdot π \cdot \sqrt{\frac{L_{b}}{g_{g}}}

period of a simple pendulum

T_{p} = 2 \cdot π \cdot \sqrt{\frac{L_{p}}{g_{e}}}

period of a simple pendulum(pendulum)