In 1971, Apollo astronaut David Scott dropped a hammer and a feather on the surface of the moon; and as expected, both hit the ground at the same time. This implies that the period, T, of a simple pendulum is not affected by its weight.
T = 2 pi sqrt( L / g ) , where g = 9.8
If T = 1 second then the length of the string will be (Excel)
L = 9.8/((2*PI())^2) = 0.248237
or about 0.25 meters.
Regardless of how carefully the theory is derived, everything must be verified by experiment. See www.online-stopwatch.com for a timer.
I start the timer and count the moving cup for 50 cycles. The timer indicates 49.537 seconds, which is close to the expected value of 50.00 seconds.
Broomstick PendulumThe laws of motion are general and ubiquitous. With some effort, a modified formula for a cylindrical object is derived, as before, only the measurement, L, is required.
= 1.8175 seconds
So after 30 cycles the elapsed time should be 54.525. My stopwatch says 54.185 seconds. Do try it at home!