Simple Harmonic Motion and Waves
Name____________________ Per___
DEFINITIONS
Periodic Motion:
Simple Harmonic Motion (SHM):
Period
Frequency
Amplitude
Equilibrium Position
Displacement
Ex 1: A fishing bobber moves up and down 24 times in 1 minute.
A: What is its period?
B: What is its frequency?
C. What is the relationship between period and frequency?
SPRINGS:
Most mass-spring systems obey a direct relationship between force and displacement. This relationship is
described by
Hooke’s Law
Fs = kx
Where
Fs: spring force (N)
*Sometimes referred to as elastic force
K: spring constant (N/m)
X: displacement (m)
Ex 2:
A.
B.
C.
D.
Sauder
I have a slinky with a spring constant of 130 N/m. With what force do I need to pull it to stretch
the slinky from its equilibrium position for the following displacements?
0.1m:
0.5 m:
What is the relationship between Force and displacement?
How would the required force (to displace the mass 0.1m) change if the spring constant was
doubled?
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Simple Harmonic Motion and Waves
Name____________________ Per___
SPRINGS & SHM:
Ts  2
m
k
Where
Ts: Period of a spring force (sec)
K: spring constant (N/m)
m: mass (kg)
What is the relationship between mass and period of a spring?
What is the relationship between spring strength (Think spring constant) and period of a spring?
Ex 3: What is the mass of my car if the shocks have a spring constant of 6000 N/m and it oscillates
with a period of 2 seconds when I hit a bump in the road?
A.The ____________________ is the time of one
complete vibration.
B.The ____________________ of vibratory motion
is the number of vibrations per second.
C.The frequency is the ____________________ of
the period.
T
sec onds
cycles
f 
cycles
sec ond
Sauder
An object suspended so that it can swing back and forth about
an axis is called a ___________________.
An ideal pendulum is one where all mass is considered to be
concentrated in the __________.
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Simple Harmonic Motion and Waves
Tp  2
Name____________________ Per___
l
g
Where
Tp: Period of a pendulum (sec)
l: length of pendulum (m)
g: acceleration due to gravity (m/s2)
Refer to the pendulum formula and answer the following statements:
 How does mass affect period?
 What is the relationship between length and period?
 What is the relationship between acceleration of gravity and period?
Ex 4:
What is the period of a pendulum that is 0.35 m long at sea level?
Ex 5:
The frequency of a moving pendulum measures 23 oscillations per 4.3 seconds. Determine
the length of such pendulum.
Ex 6:
How do the periods of two pendulums compare if one has a measure of 25 cm and the other
has a measure of 100 cm?
References:
Trinklein, F. E. Modern Physics (TE). Austin: Holt, Rinehart and Winston, 1992.
Section 6.2 of Zitzewitz, P. W. Glencoe Physics: Principles and Problems. New York:
Glencoe/McGraw-Hill, 2002.
Sauder
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