The document discusses simple pendulums and calculating their periods. It provides information on measuring the period of pendulums with different masses and lengths to check that period only depends on length and gravity. An example calculates the period of a 40 cm pendulum and where it will be 6 seconds later. Exercises calculate the period of a 10 cm pendulum and the string length needed for a pendulum currently with a 0.75 m string to have a period of 2 seconds.

1. Research time
Calculate the sine from 0,5,10,15,20,25,30,35,40 degrees
x in degree 0 5 10 15 20 25 30 35 40
sin(x)
x in rad

2. Simple pendulum
Always true for Simple Harmonic Motion (SHM):
The restoring force equals to:
From the second law of motion:
The displacement equals to:

3. Simple pendulum
The period of simple pendulum depends only on the Length of the string and g!
Let's Check it!
Measure the period of simple pendulum with different masses
Time (s) Number
of cycles
Period (s) Average
period (s)
Length of a
string (m)
Mass
(kg)

4. Example
As illustrated in the figure, a simple pendulum of length 40
cm is oscillating over a small displacement about its
equilibrium position.
a) What is the period of the pendulum?
b) If the pendulum starts oscillating from point A, at which
point will it be 6 s later? (Take g=10 m/s2, π = 3)

5. Exercise
Calculate the period of a simple pendulum with string length of 10 cm.
(Take g = 10N/kg)

6. Exercise
A simple pendulum has a string of length 0.75 m and a period of 1 s. How long
should the string of the pendulum be, for its period to be 2 s, at the same location?