Find the length of a pendulum that oscillates with a frequency of 0.40 Hz Answer in meters

You need to remember the formula of period of pendullum for small amplitudes such that:

`T~~2pi*sqrt(L/g)`

L expresses the pendulum length

g expresses the acceleration of gravity`~~9.8 m/(s^2)`

You need to remember that `T = 1/F`

F expresses the frequency

`T = 1/0.4 =gt T = 10/4 =gt T =...

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You need to remember the formula of period of pendullum for small amplitudes such that:

`T~~2pi*sqrt(L/g)`

L expresses the pendulum length

g expresses the acceleration of gravity`~~9.8 m/(s^2)`

You need to remember that `T = 1/F`

F expresses the frequency

`T = 1/0.4 =gt T = 10/4 =gt T = 5/2 = 2.5 s`

You need to substitute 2.5 s for T in equation of period above such that:

`2.5 = 2pi*sqrt (L/9.8) =gt sqrt (L/9.8) = 2.5/(2pi)`

You need to raise to square both sides such that:

`L/9.8 = (2.5/(2pi))^2`

`L = 9.8*(2.5/(2pi))^2`

`L = 1.5514 m`

Hence, evaluating the length of pendulum in meters yields`L = 1.5514 m.`

Approved by eNotes Editorial Team