A simple pendulum has a length 4 times the length of another pendulum. The ratio of the periods of the longer pendulum compared to that of the shorter one is​

Time period T of a pendulum of length l is given by ,

T=2π

l/g

,

for pendulum 1 ,

T

1

=2π

l

1

/g

for pendulum 2 ,

T

2

=2π

l

2

/g

, 1

given l

1

=4l

2

,

therefore , T

1

=2π

4l

2

/g

, 2

dividing 2 by 1 , we get

T

1

/T

2

=

4

=2 ,

or T

1

=2T

2

resonant frequency