Prepare for your exams
Get points
Guidelines and tips

Sell on Docsity

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study

Go to the blog

Simple Harmonic Motion: A Comprehensive Guide for Students, Lecture notes of Physics

University of Pittsburgh (Pitt) - Medical Center-Health System Physics

The spring is neither stretched nor compressed. (b) The object is displaced and the spring is stretched. • When the restoring force is directly proportional to ...

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

ahalya 🇺🇸

4.9

(16)

257 documents

1 / 3

This page cannot be seen from the preview

Don't miss anything!

SIMPLE'HARMONIC'MOTION!

Created!by:!Binh!Cao!

!!! ! !!

• Simple'harmonic' motion!(SHM)!is!a!type!of!periodic!motion.!Two!simple!systems!of!SHM!

that! are! mainly! discussed! in! college! are! an' ideal' spring!and! a' simple' pendulum.! But!

before!discussing!these!2!systems,!it!is!essential!to!go!over!periodic!motion!first.'

• Periodic'motion!or!oscillation!refers!to!kinds!of! motion!that!repeat!themselves!over!and!

over.!For!example,!a!clock!pendulum.!

• Understanding! periodic! motion! is! critical! for! understanding! more! complicated! concepts!

like!mechanical!waves!(e.g.!sound)!and!electromagnetic!waves!(e.g.!light)!

• Oscillation! is! characterized! by! an! equilibrium!and! a! restoring' force.! At! equilibrium,!

restoring! force! on! the! object! is! zero.! When! the! object! is! displaced! from! equilibrium,! a!

restoring!force!acts!on!the!object!to!restore!its!equilibrium.!For!example,!a!spring.!

!

(a) The!object!is!at!equilibrium.!The!spring!is!neither!stretched!nor!compressed.!

(b) The!object!is!displaced!and!the!spring!is!stretched.!

• When! the! restoring! force! is! directly! proportional! to! displacement! from! equilibrium,! the!

oscillation!is!called!simple'harmonic'motion!(SHM).!!

• Important!characteristics!of!any!periodic!motion:!

o Amplitude'(A)!is!maximum!magnitude!of!displacement!from!equilibrium!

o Period'(T)!is!the!time!to!complete!one!cycle!(unit:!s)!

o Frequency!(f)!is!the!number!of!cycles!in!a!unit!of!time!(unit:!sN1)!

o Period!and!frequency!are!related!by!the!following!relationship:!

𝑇=

1

𝑓!𝑜𝑟!𝑓=

1

𝑇!

o Angular'frequency!(ω):!!

𝜔=2𝜋𝑓 =!!

!!(rad/s)!

A/'Ideal'spring'

𝐹

!"#$%!&'( =−𝑘𝑥!!

Partial preview of the text

Download Simple Harmonic Motion: A Comprehensive Guide for Students and more Lecture notes Physics in PDF only on Docsity!

Created by: Binh Cao

Simple harmonic motion (SHM) is a type of periodic motion. Two simple systems of SHM that are mainly discussed in college are an ideal spring and a simple pendulum. But before discussing these 2 systems, it is essential to go over periodic motion first.
Periodic motion or oscillation refers to kinds of motion that repeat themselves over and over. For example, a clock pendulum.
Understanding periodic motion is critical for understanding more complicated concepts like mechanical waves (e.g. sound) and electromagnetic waves (e.g. light)
Oscillation is characterized by an equilibrium and a restoring force. At equilibrium, restoring force on the object is zero. When the object is displaced from equilibrium, a restoring force acts on the object to restore its equilibrium. For example, a spring. (a) The object is at equilibrium. The spring is neither stretched nor compressed. (b) The object is displaced and the spring is stretched.
When the restoring force is directly proportional to displacement from equilibrium, the oscillation is called simple harmonic motion (SHM).
Important characteristics of any periodic motion: o Amplitude (A) is maximum magnitude of displacement from equilibrium o Period (T) is the time to complete one cycle (unit: s) o Frequency (f) is the number of cycles in a unit of time (unit: s-‐^1 ) o Period and frequency are related by the following relationship: 𝑇 =

o Angular frequency (ω): 𝜔 = 2 𝜋𝑓 = !! ! (rad/s) A/ Ideal spring 𝐹!"#$%!&'( = −𝑘𝑥

Created by: Binh Cao k: spring constant x: displacement from equilibrium 𝜔 = ! !

! !!

! !! ! !

! !

!! !

! ! 𝑥 = 𝐴 cos(𝜔𝑡 + 𝛷) Φ: initial angular displacement 𝐸 = ! !

𝑚𝑣!^!^ +

! !

𝑘𝑥!^ =

! !

𝑘𝐴!^ = 𝑐𝑜𝑛𝑠𝑡

E: mechanical energy of the system 𝑣!: velocity of mass m at x (m/s) B/ Simple pendulum 𝐹!"#$%!&'( = −𝑚𝑔𝑠𝑖𝑛𝜃 ≅ −𝑚𝑔𝜃 (when θ is small) Θ: angular displacement form equilibrium 𝜔 = ! !

! !!

! !! ! !

! !

!! !

! ! L: string length (m) C/ Examples 1/ When a body of unknown mass is attached to an ideal spring with force constant 120 N/m, it is found to vibrate with a frequency of 6.00 Hz. Find (a) The period of the motion; (b) The angular frequency; (c) The mass of the body. Solution: k = 120 N/m; f = 6.00 Hz (a) 𝑇 = ! !

! !.!!

(b) 𝜔 = 2 𝜋𝑓 = 2 𝜋× 6. 00 = 37. 7 (rad/s) (c) 𝜔 = ! ! or 𝑚 = ! !!^

!"# !".!!^