Learning Activity Sheet in General Physics 1 Lesson 11: Periodic Motion
Learning Activity Sheet in General Physics 1 Lesson 11: Periodic Motion
Learning Activity Sheet in General Physics 1 Lesson 11: Periodic Motion
CONTENT STANDARDS:
GRAVITATION: The learners demonstrate an understanding of...
1. Periodic Motion
2. Simple harmonic motion: spring- mass system, simple pendulum, physical
pendulum
3. Damped and Driven oscillation
4. Periodic Motion experiment
5. Mechanical waves
PERFORMANCE STANDARDS:
Solve multi- concept, rich context problems using concepts from rotational motion,
fluids, oscillations, gravity, and thermodynamics
1. Relate the amplitude, frequency, angular frequency, period, displacement, velocity, and acceleration of
oscillating systems . (STEM_GP12PM-IIc-24).
2. Recognize the necessary conditions for an object to undergo simple harmonic motion (STEM_GP12PM-
IIc-25)
3. Analyze the motion of an oscillating system using energy and Newton’s 2nd law approaches
(STEM_GP12PM- IIc-26)
4. Calculate the period and the frequency of spring mass, simple pendulum, and physical pendulum
(STEM_GP12PM- IIc-27 )
5. Differentiate underdamped, overdamped, and critically damped motion (STEM_GP12PM- IId-28 ).
6. Describe the conditions for resonance (STEM_GP12PM- IId-29)
7. Perform an experiment involving periodic motion and analyze the data—identifying discrepancies between
theoretical expectations and experimental results when appropriate (STEM_GP12PM- IId-30)
8. Define mechanical wave, longitudinal wave, transverse wave, periodic wave, and sinusoidal wave
(STEM_GP12PM- IId-31)
9. From a given sinusoidal wave function infer the (speed, wavelength, frequency, period, direction, and
wave number (STEM_GP12PM- IId-32)
10. Calculate the propagation speed, power transmitted by waves on a string with given tension, mass, and
length (1 lecture) (STEM_GP12PM- IId-33)
Many events in both nature and technology are periodic, with a certain motion repeating
itself over and over again. As its name suggests, simple, harmonic motion, is the most
basic kind of oscillation. A tree swaying in the wind, a child on a swing, the pistons of a
car engine, the vibrating atoms in a solid-all are undergoing simple harmonic motion, or
very nearly so. In fact, every periodic event is either simple harmonic or else the result of
several such motions mixed together.
In harmonic motion the energy of the vibrations goes back and forth between kinetic and
potential forms. The potential energy may be elastic rather than gravitational; we will find
later that the notion of potential energy has even wider scope. The electrical equivalent
of potential energy, in particular, can lead to electrical equivalent of potential energy, in
particular, this oscillations that make possible the electronic recording and transmission
of sight and sound.
Brief Discussion
Open the lid of a jack-in-the-box and out pops jack. How fast does he move? How
high does he go? Not a very dignified problem for a serious science like physics, one
might think, but the principles behind a jack-in-the-box apply equally well to any other
system that stores elastic potential energy.
When we pull out a spring, it resists being stretched, and if we then let go, the
spring returns to its original length. As we know, this is typical of elastic behavior. On the
other hand, when we pull out a piece of taffy, it also resists being stretched, but if we then
let go nothing happens: the deformation is permanent. This is typical of plastic behavior.
In the case of the stretched spring, a restoring force comes into being that tries to
return the spring to its normal length. The more we stretch the spring, the more the
restoring force we must overcome. Exactly the same thing happens when we compress
the spring: It resists being shortened, and if we let go, the spring goes back to its normal
length. Again, a restoring force arises, and again the more the compression, the more
the restoring force to be overcome.
The amount x by which an elastic solid is stretched or compressed by a force is
directly proportional to the magnitude F of the force, provided the elastic limit is not
exceeded. This proportionality is called Hooke’s law.
F=kx
Where k is a constant whose value depends on the nature and dimensions of the
object. A stiff spring has a higher value of k than a weak one.
Total energy = KE + PE
hence,
v=(2)(pie)(f) √A^2 – x^2) speed at given displacement
A simple pendulum is one which can be considered to be a point mass suspended from a string or
rod of negligible mass. It is a resonant system with a single resonant frequency. For small
amplitudes, the period of such a pendulum can be approximated by: Show. For pendulum length.
For small amplitudes, the period of a physical pendulum only depends on the moment of inertia of
the body around the pivot point and the distance from the pivot to the body's center of mass. It is
calculated as: T=2π√Imgh T = 2 π I mgh . The period is still independent of the total mass of the
rigid body.
Exercises
DIRECTIONS: Multiple Choice. One (1) point for each number. Select the correct
answer from the given choices. Shades your answer on the answer sheet provided.
1. The product of the period and the frequency of a harmonic oscillator is always
equal to?
A. 1 B. pie
C. 2pie D. The amplitude of the motion
7. An object undergoes simple harmonic motion. Its maximum speed occurs when
its displacement from its equilibrium position is?
A. Zero B. A maximum
C. Half its maximum value D. None of the above
10. A pendulum comes very close to executing simple harmonic motion provided
that?
A. Its bob is not too heavy B. The supporting string is not too
long
C. The arc trough which it swings is D. The arc through which it swings
not too small is not too large.
12. A pendulum clock is in an elevator. The clock will run fast when the elevator is?
A. Rising at constant speed B. Falling at constant speed
C. Accelerating upward D. Accelerating downward
13. An object pivoted at an arbitrary point swings back and forth with the period T.
the number of other points in the object at which it can be pivoted and have the
same period is?
A. 0 B. At least 1
C. At least 2 D. Unlimited
15. S spring whose force constant is k is cut in half. Each of the new springs has a
force constant of
A. ½ k B. K
C. 2k D. 4k
16. A string force constant 1.0 N/m is joined end-to-end to a spring of force constant
2.0 N/m. the force constant of the combination is?
A. 0.67 N/m B. 1.0 N/m
C. 1.5 N/m D. 3.0 N/m
17. A force of 0.2 N is needed to compress a certain spring by 2 cm. its potential
energy when compress is?
A. 2 X 10-3 J B. 2 X 10-5 J
C. 24X 10-5 J D. 8 X 10-5 J
18. A 0.40 lb toy car is pressed against a horizontal spring of force constant 12.0
lb/ft. the spring is compressed 1.5 in and then the car is let go. If there is no
friction, the car leaves the spring with a speed of
A. 0.68 ft/s B. 3.9 ft/s
C. 11 ft/s D. 46 ft/s
19. When a 1.0 kg mass is suspended from a spring, the spring stretches by 50
mm. the force constant of the spring is?
A. 0.20 N/m B. 1.96 N/m
C. 49 N/m D. 196 N/m
20. If the suspended mass of multiple choice 19 oscillates up and down, its period
will be approximately?
A. 0.032 s B. 0.071 s
C. 0.45 s D. 4.5 s
Note: This will be your answer sheets for all the exercises that you need to answer in the
succeeding lessons. You are allowed to photocopy this.
Reflection
DIRECTIONS:
1. At what point or points in its motion is the energy of a harmonic
oscillator entirely potential? At what point or points is its energy
entirely kinetic?
2. A wooden object is floating in a bathtub. It is pressed down and the
released. Under what circumstances will its oscillations be simple
harmonic in natures?
Rubrics
Short 4 3 2 1
Answer All the key Most of the 2 of the key 1 of the key
Essays words are key words are words are words is
presented, presented, presented, presented,
and each are and each are and are and is
explained. explained. explained. explained.
References
Crisostomo, A.L. and Reyes, S.B. (2015). Physics Laboratory Manual. Revised
Edition. National Bookstore
Prepared by:
RONIE B. SARCOS
WILNELIA C. BALINGTON
Master Teacher I-SGH-Science