Question

EVERYONE WHO ANSWERS RIGHT GETS MEDALS!!!!
If a pendulum with length 169 cm has a frequency of 1/20 Hz, find the length of a pendulum that has frequency 1/5 Hz, given that you know that the frequency varies inversely with the square root of the length.

Answer 1

169 ---- 1/20 Hz
x ----- 1/5 Hz
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x=(169 x 1/5)/1/20 = (169 x 20)/5 =169 x 4 = 42,2 cm

Answer 2

I think using the formula of simple pendulum

T = 2pi * squrt(L/g) to solve for g
20 = 2pi * squrt(1.69/g) => g= 1.69 * (2pi/20)^2=0.1668 m/s^2
then
5 = 2pi* squrt(L/0.1668) => L= (5/2pi)^2*0.1668 = 0.106 m = 10.6 cm