A pendulum is a weight suspended from a
pivot so that it can swing freely.
Small-angle
approximation
If it is assumed that the oscillation's angle is much less than 1
radian the period of swing is approximately the same for
different size swings: that is, the period is independent of
amplitude. This property, called
isochronism, is the reason pendulums are so useful for timekeeping.
Successive swings of the pendulum, even if changing in amplitude, take
the same amount of time:
where T is the period of swing,
g is the acceleration
due to gravity and l
is the lenght of the pendulum.
1-Isochronism: for small swings, the period of swing is approximately the same for
different size swings: that is, the period is independent of
amplitude
2-For pendulums of length L the period of
oscillations is the same regardless of the mass M of the suspended
particle .
1)Calculate the period of oscillation of a simple pendulum,
1.5m long, on the moon.
I dont have the acceleration due to gravity on the moon. I
searched a value on the internet. I found g = 1, 63 m/s
^{2}. So:
2) Find the length of the pendulum which has a specified
period. We use this formula:
Example: build a pendulum that beats the second (i.e. , we need to
find the length of the pendulum that has the period to 1 sec). In
Italy g=9.8m/s ^{2}.
3)Measure the acceleration due to gravity in a certain place of
the Earth
example:
these are the results of measurements of 10 complete
oscillations made from a 3 m long pendulum:
T1=35.2s,T2=34.6s, T3=34.4s. Calculate the acceleration
due to gravity. Calculate the average of the
measurements, then divide by 10