A simple pendulum in a seismometer

1. A T R A D I T I O N A L
P E N D U L U M S E I S M O M E T E R
C H I N - V E R N TA N ; PA Y S 1 0 1 ; S E C T I O N 2 0 2

2. H O R I Z O N TA L
M O T I O N I N A
S E I S M O M E T E R
• The seismometer consists of a heavy mass
hung by a string that counters the force of
gravity and thus, holds the mass in a fixed
position
• The mass is able to measure the movement
of the ground if it moves in a horizontal
direction, thus indicating an earthquake
• Thus, the pendulum will move in a motion
that is described as simple harmonic
motion

3. A S E I S M O M E T E R , C O N S I S T I N G O F A
S I M P L E P E N D U L U M T H AT I S M A D E
O F A 1 0 0 K G M A S S AT TA C H E D T O 5 M
O F M A S S L E S S S T R I N G , I S
U N D E R G O I N G S I M P L E H A R M O N I C
M O T I O N W I T H A M A X I M U M A N G U L A R
D I S P L A C E M E N T O F 3 0 D E G R E E S .
A ) W H AT I S T H E P E R I O D O F T H E
P E N D U L U M ?
B ) W H AT I S T H E R E S T O R I N G F O R C E
N E E D E D T O B R I N G T H E P E N D U L U M
B A C K T O T H E E Q U I L I B R I U M P O I N T ?
O U R Q U E S T I O N

4. Let’s tackle Part A of the question that asks us to find the period of the
pendulum.
The period of the pendulum can be found by
L is the length of the massless string, which is 5m.
g is the acceleration due to gravity, which is 9.80m/s^2 on Earth.
Thus, T=2pi*sqrt(5/9.8)
=4.49s
The period of the pendulum is 4.49 seconds.

5. Now let’s look at the second part of the question, which asks us to find the restoring
force needed to bring the mass back to its equilibrium point.
We can use the equation
We know that the maximum angular displacement is 30 degrees, which corresponds
to pi/6 rads. We also know the mass is 100kg and acceleration due to gravity is
9.8m/s.
Thus, we can find the restoring force needed.
Fnet= -(100kg)(9.8m/s^2) sin (pi/)
=-490N
490 N is needed to restore the mass back to its equilibrium position.

6. C O N C L U S I O N
It is incredibly interesting to note that the first
seismometer consisted of a pendulum and using
simple harmonic motion to find characteristics of
the motion caused by the earthquake. This shows
how physics is instrumental to understanding
natural events.