Question

Your grandfather clock’s pendulum has a length of 0.9930 m. if the clock runs slow and loses 21 s per day, how should you adjust the length of the pendulum?

Answer 1

If your clock is running to fast, you lengthen the pendulum to slow it down. A grandfather's clock normally has screw with a nut at the bottom of the bob on the pendulum. You can screw the nut a turn or so and lengthen the pendulum by one thread on the screw.

If the clock runs 0.75 minute fast each day, that means is it running

0.75 minute / day x (1 day / 24 hrs) x (1 hr / 60 min) = 0.000521 fractionally fast

To make Square Root (L/g) increase by 0.000521, you must make
the increase length, delta

delta = 2 x 0.000521 x L (can you verify why this is true? In particular why does the square root
give the factor of two for the small increase?)

Thus, you must lengthen the pendulum by
delta = 1.03 mm  

               If your clock is running to fast, you lengthen the pendulum to slow it down. A grandfather's clock normally has screw with a nut at the bottom of the bob on the pendulum. You can screw the nut a turn or so and lengthen the pendulum by one thread on the screw.

If the clock runs 0.75 minute fast each day, that means is it running

0.75 minute / day x (1 day / 24 hrs) x (1 hr / 60 min) = 0.000521 fractionally fast

To make Square Root (L/g) increase by 0.000521, you must make
the increase length, delta

delta = 2 x 0.000521 x L (can you verify why this is true? In particular why does the square root
give the factor of two for the small increase?)

Thus, you must lengthen the pendulum by
delta = 1.03 mm  

               If your clock is running to fast, you lengthen the pendulum to slow it down. A grandfather's clock normally has screw with a nut at the bottom of the bob on the pendulum. You can screw the nut a turn or so and lengthen the pendulum by one thread on the screw.

If the clock runs 0.75 minute fast each day, that means is it running

0.75 minute / day x (1 day / 24 hrs) x (1 hr / 60 min) = 0.000521 fractionally fast

To make Square Root (L/g) increase by 0.000521, you must make
the increase length, delta

delta = 2 x 0.000521 x L (can you verify why this is true? In particular why does the square root
give the factor of two for the small increase?)

Thus, you must lengthen the pendulum by
delta = 1.03 mm