GENERAL PHYSICS 1_QUARTER 2_WEEK 3

Oscillatory Motion
and Waves
Present by:
Group 3
 OBJECTIVES

• At the end of this report, you should be able to:

K: Explain the differences of the different types of waves
and
motion;
S: Solve the characteristics (amplitude, wavelength, period,
frequency, and intensity) of a wave; and
A: Relate the importance of waves and motion in daily life.
 LEARNING COMPETENCIES

• Relate the amplitude, frequency, angular frequency, period, displacement,

velocity, and acceleration of oscillating systems.
• Recognize the necessary conditions for an object to undergo simple harmonic
motion.
• Calculate the period and the frequency of spring mass, simple pendulum, and
physical pendulum.
• Differentiate underdamped, overdamped, and critically damped motion.
• Define mechanical wave, longitudinal wave, transverse wave, periodic wave, and
sinusoidal wave.
• Infer the speed, wavelength, frequency, period, direction, and wave number from
a sinusoidal wave function.
What’s your favorite musical
instrument?

Whether it is a guitar, a violin, a piano, a flute,

the same concept in waves and acoustic can
explain how they work.
Oscillation and Periodic Motion
of a Pendulum

Waves
Water Waves

An oscillation or vibration is a
“wiggle” in time. An example is the
periodic motion of a pendulum where
Sound Waves
the bob sings back and forth. A wave,
on the other hand, is a “wiggle” in
both space and time. Some examples
are water waves, sound waves,
waves on a string, and Electromagnetic
Wave
electromagnetic waves.
Waves on a String
 The relationship between
Oscillation and frequency and period is

Waves
Frequency and period are reciprocals. If
the frequency is 60 Hz, the period is
1/60 (or 0.017). If the period is 0.010 s,
the frequency is 100 Hz. Frequency (f)
is defined to be the number of events SI Unit for Frequency: cycle per
second; defined to be Hertz
per unit time. For periodic motion,
(Hz)
frequency is the number of oscillations
per unit time.
 EXAMPLE:
Oscillation and Calculate the frequency
Waves and its period if a pendulum
completes 30 cycles in 15
seconds. Given:
Cycle = 30
A cycle is one complete t = 15 s
SOLUTION:
oscillation. Note that a vibration
can be a single or multiple event,
whereas oscillations are usually
repetitive for a significant number
of cycles.
Simple Harmonic Motion: A Special
Periodic Motion

Objects that move back and forth over the same path
such as a swinging pendulum, a metal weight bobbing
up and down, and a vibrating guitar spring exhibit
periodic motion. One type of periodic motion is simple
harmonic motion. Simple harmonic motion is an
oscillatory motion experienced by an object displaced
by a force from an equilibrium position.
Simple Harmonic Motion: A Special
Periodic Motion
- Like any other motion, can be described in terms of
displacement, velocity, and acceleration.
- A body whose acceleration is proportional to its
displacement from a certain equilibrium position and opposite
to its displacement is said to move in simple harmonic motion.
- A body moving in SHM has its displacement attained by the
body on either side of the equilibrium is its amplitude. The
total number of vibrations per unit time is called frequency of
the motion. On the other hand, the time for one complete
vibration is called period of motion.
Simple Harmonic Motion: A Special
Periodic Motion

Equations for Simple Harmonic Motion

 SOLUTION:
Simple Harmonic Motion:
A Special Periodic Motion
EXAMPLE:

A 100-g body is attached at the end of a

hanging spring with a spring constant of
2,000 dynes/cm. It is displaced 10 cm from
its equilibrium position and then released.

(a) calculate the period (T)

(b) find the maximum acceleration of the
body, and
(c) find the acceleration of the body when it
is 5.0 cm from the equilibrium position.
 SOLUTION:
Simple Harmonic Motion:
A Special Periodic Motion
EXAMPLE:

A 100-g body is attached at the end of a

hanging spring with a spring constant of
2,000 dynes/cm. It is displaced 10 cm from
its equilibrium position and then released.

(a) calculate the period (T)

(b) find the maximum acceleration of the
body, and
(c) find the acceleration of the body when it
is 5.0 cm from the equilibrium position.
 SOLUTION:
Simple Harmonic Motion:
A Special Periodic Motion
EXAMPLE:

A 100-g body is attached at the end of a

hanging spring with a spring constant of
2,000 dynes/cm. It is displaced 10 cm from
its equilibrium position and then released.

(a) calculate the period (T)

(b) find the maximum acceleration of the
body, and
(c) find the acceleration of the body when it
is 5.0 cm from the equilibrium position.
THANK YOU FOR
LISTENING!
SPRING MASS
OSCILLATOR
When Dealing with problems in a spring
mass motion, you must remember the
following:

• The gravitational field strength is not a factor affecting the time period.

• Amplitude does not affect the time period, it doesn’t matter how far
mass is from the equilibrium point, it will still move up and down or
back and forth with the same time period.

• The mass of the spring affects the number of time periods. An increase
in mass means longer period in the spring mass motion.

• For you to decrease the period, you must increase the stiffness of the
spring.
FORMULA:

√
WHERE:
𝑚
𝑇 =2 𝜋 T= time period measured in s (second)
𝑘 2= is constant
π = is 3.14159 and is constant
m= mass of the spring measured in
kg (kilogram)
k= spring constant, N/m (Newton
per meter)
Additional Variables
F= frequency, measured in Hz
radiance/sec or rad/s

How are these variables proportional to each other?

• Time (T) is Proportional to the

• Time (T) is proportional to
Question: if the k (spring constant) increase by 4, what
will happen to the time period?

Answer: If the k is going up by the factor of 4 and time (T) is proportional to

. Therefore,

Since 2 is a denominator, therefore time period decreases

by 2.
Example:
A horizontal spring k (k=300 N/m) with a mass of 0.75 kg attached to it is
undergoing simple harmonic motion.
Calculate:
a.Period
b.Frequency
c.Angular velocity
THE SIMPLE PENDULUM

A Simple pendulum consist of a bob of relatively

large mass hanging on a string with negligible mass.
The string is normally in a vertical position. The bob
hangs along a vertical line and is in equilibrium
under the action of two forces, its weight and the
tension in the string.
Pendulums are in common usage. Some have
crucial uses, such as in clocks; some are for fun,
such as a child’s swing; and some are just there,
such as the sinker on a fishing line.
Equation in solving Simple Pendulum:

Where:
T= time period measured in s (second)
2= is constant ADDITIONAL VARIABLES:
π = is 3.14159 and is constant f= Frequency, measured in
l= length Hz
g= gravitational field a strength= 9.8
m/s
How are these variables proportional to eacht other?
Time period is proportional to the length of the pendulum as it is with the
gravitational field strength .
Example”
A string of a pendulum has a length of 1.0 m and has a peiod of 2.0 s. Find
the value of g at a point of the pendulum. If the same pendulum is brought to
another place where the value of g is 9.85 m/s, what is the period of the
pendulum at the place?
Solution (a):
Given: and solved for g:

L = 1.0 m
T= 2.0 s

2. Substitute known values into the equation:

(a)Value of g at a point ‘
(b)T of the pendulum at a point
where g is equal to 9.85 m/s
PHYSICAL PENDULUM (PP)

A Physical pendulum refers to an object which oscillates back and forth, in contrast to
the rather idealized simple pendulum where all the mass is concentrated in a single point
(usually the mass hanging on the end of the massless rope). One example of a physical
pendulum is a baseball bat swinging back and forth. Any object which is acted upon by a
restoring torque will move in angular harmonic motion when given an angular displacement.
A physical pendulum can illustrate this effect.

When a disk is displaced in such a way that there is a restoring torque, we have a
torsion balance. The restoring torque tends to bring it back to its equilibrium position. The
body is said to move with angular harmonic motion. The body is free to rotate about an axis
perpendicular to its own plane.
Equation in solving Physical Pendulum

T
Example: A body is pivoted so that its center of gravity is 1.0 m from
the axis of rotation. The body's radius of gyration is 60 cm. The body
acts like a physical pendulum. Find the period of vibration of the
body.

Given:
Center of gravity of the body = 1.0 from the axis of rotation
Radius of gyration = 60 cm
Required:
Period T of the body
Solution:
T

T= 1.2s
 AN INTRODUCTION TO

undernamped,
overdamped, and
critically damped
motion
 UNDERNAMPED

It refers to the movement of an object in a

system which returns to equilibrium position
faster but overshoot and cross over one or more
times until it reaches the displacement (x) as
shown in Figure 1.
 OVERDAMPED

• It refers to the slow movement of an object in a

system which returns to equilibrium. It (B)
moves more slowly toward equilibrium than in
the critically damped system as shown in
Figure 2.
 CRITICALLY DAMPED
MOTION
• A system is called critically damped if the
object (A) returns the system to equilibrium as
fast as possible without overshooting. Like
automatic door and window closer
mechanisms, they promptly come to original
positions without showing any further
oscillations. It is the limit if damping ratio
reduced overshooting this limit, then system
will show oscillating equilibrium.
THANKYOU!!
hehehehe
SINUSOIDAL
WAVES
Sine wave, a repetitive oscillation with
smooth curves, is defined as having
amplitude proportional to displacement
angle, and can be created by combining
sine waves.
SINUSOIDAL FUNCTION
 Waves are characterized by the
motion of particles in the medium,
which can be mathematically described
using wave functions or sinusoidal
functions to calculate position,
velocity, and acceleration.
 PULSE

A wave is a single disturbance with constant

amplitude, propagating at a constant speed,
preserving its structure and calculating the
pulse's distance in time.
Every 2π radians, a sine function
oscillates between +1 and -1.
Consider the ratio of the angle and the
location when building our wave model with
a periodic function:
• an oscillatory motion experienced by an object displaced by a force from an
equilibrium position. Simple Harmonic Motion: A Special Periodic Motion
• Write the equation for simple harmonic motion
• An oscillation or vibration is a “wiggle” in time.
• A cycle is one complete oscillation.
• Frequency and period are reciprocals. If the frequency is 60 Hz, the period is
1/60 (or 0.017)