PHY131H1F - Class 20Today:

• Today, Chapter 13:

• General Periodic

Oscillations

• Special case:

Simple Harmonic

Motion

Animation from http://www.uni-saarland.de/fak7/knorr/homepages/patrick/theorex/MapleScripts/oscillations/forced_oscillations1.html

• A construction worker of mass mw

sits 2.0 m from the end of a steel

beam of mass mb, as shown.

• The tension in the Cable is T

• The wall exerts a normal force, n on

the beam, and an upward force, F1.

• Define +x = to the right, +y = up,

and the pivot is the point where the

beam touches the wall.

• What is the normal force, n? A. (mb + mw)g

B. (mb + mw)g − T cos(30°)

C. (mb + mw)g − T sin(30°)

D. T sin(30°)

E. T cos(30°)

T

mwg

mbg

F1

n

6.0 m

• A construction worker of mass mw

sits 2.0 m from the end of a steel

beam of mass mb, as shown.

• The tension in the Cable is T

• The wall exerts a normal force, n on

the beam, and an upward force, F1.

• Define +x = to the right, +y = up,

and the pivot is the point where the

beam touches the wall.

• What is the force, F1?

T

mwg

mbg

F1

n

A. (mb + mw)g

B. (mb + mw)g − T cos(30°)

C. (mb + mw)g − T sin(30°)

D. T sin(30°)

E. T cos(30°)

6.0 m

Class 20 Preclass Quiz on MasteringPhysics

This was due this morning at 8:00am

91% of students got: What term denotes the time for one

cycle of a periodic process? Period.

96% of students got: For vibrational motion, what term

denotes the maximum displacement from the equilibrium

position? Amplitude.

93% of students got: A mass on the end of a spring

undergoes simple harmonic motion. At the instant when the

mass is at its maximum displacement from equilibrium, its

instantaneous velocity is zero.

Class 20 Preclass Quiz Student Comments

“i miss those simple days were the only physics you had to

know was speed=distance/time.”

“What is the force on the mass at the equallibrium point?”

Harlow answer: zero. Equilibrium is defined as Fnet = 0. If

the mass was at rest there, it would stay at rest.

“What's the difference between period and wavelength?”

Harlow answer: Period is the distance between crests on a

plot of y vs t (sometimes called a “history graph”), and

wavelength is the distance between crests on a plot of y vs x

(sometimes called a “snapshot graph”). Anything that is

oscillating has a period, but only waves have wavelength.

“i always used to play with rulers on the edge of the table as

a kid and it annoyed everyone, so that example in the book

really spoke to me.”

Class 20 Preclass Quiz Student Comments

“My confidence level in this course can be modelled as a

periodic function. The crests (max confidence) occur right

before a term test and the troughs (min confidence) occur

once the marks are given back.”

“I still did pretty badly on the Physics test, but I improved 6.5

points from last time, and my dad told me he was proud of

me, so I am taking this as a victory.”

“GUYS DO THE COURSE EVALUATION k thanks”

“Ummmm.....Do we need to know how to make

spreadsheets for the final, cuz...well....seems kind of

difficult?”

Harlow answer: No. There won’t be any spreadsheet

questions on the final exam; I was just doing that in the video

to conceptually explain simple harmonic motion.

Test 2 Marks Posted

You should now see your mark

out of 32 under “My Grades” on

portal.

The raw average was 19/32 =

59%.

The instructors in this course

have decided to adjust the marks

by adding 3 points to every

student’s mark, but holding the

maximum mark to 32/32 = 100%.

The mark posted on portal is your adjusted mark.

The adjusted average and median were 22/32 = 69%.

After the adjustment, 185 students (20% of the class) got less than

16/32 (fail).

After the adjustment, 77 students (8% of the class) got 32/32 =

100%.

Test 2 Marks Posted

You will receive the long-answer part of your test in

Practicals between today and Dec. 1.

The multiple choice bubble sheet is stored in MP129 – if you

would like to review it, please stop by and ask April.

Check over the marking and compare it to the Test 2 Marking

Scheme posted on the portal.

If there has been a mistake in the marking or computation of

your mark, please bring the test to me or April Seeley in

MP129 and we will fix the mistake.

The deadline to report mistakes in the marking of Test 1 is

Dec. 9.

Class 20 Preclass Quiz Student Comments

“I have a Chem midterm today, so wish me luck :)”

Harlow response: Good luck to all CHM138 students on

tonight’s test!

“The last problem set was due to Tuesday which was

different than all others which were due to Monday :( This

significantly conflicted my weekly schedule! I wish they were

due to Friday like the beginning of semester! Why the

deadline has changed three times?”

Harlow answer: They are always right after a full cycle of

practicals – you are meant to be studying in Practicals to do

well on the problem set. They are posted 1.5 weeks in

advance so if you want to keep doing them on Friday nights

that is okay.

Class 20 Preclass Quiz Student Comments

“I HAVE BEEN SAYING THIS FOR THE PAST 4 PRE-QUIZ

COMMENTS. YOU LOOK LIKE JUSTIN TRUDEAU”

“please, I am losing hope on humanity... could you please

post this on the powerpoint... I don't want to get out of this

class with such grudge and regret..”

“That moment when seeing your comment on the screen

makes you happier than passing this course would..”

“Just out of curiosity, in your university life, what was your

biggest headache, physics?”

Harlow answer: No. I liked physics, even though it was

hard, I never dreaded the work. My biggest headache was

ENG100 Effective Writing. In retrospect it was an excellent

course, but I was not ready, and I really hated it. To tell you

the truth when the drop-date came I dropped it.

Bonus Point for Over 65% Course

Evaluation Response Rate

• An essential component of my commitment to teaching

excellence is the regular evaluation of courses by students.

• On Nov. 23 you were sent an email by

course.evaluations@utoronto.ca to evaluate PHY131H1F.

• It only takes 10 or 15 minutes to answer the questions and

enter your typed thoughts about the course.

• Your answers and thoughts are anonymous, but are very

important to me.

• I promise you that when the results become available to me

in January, I will read every comment and scrutinize the

responses to see if it can help me improve the course or my

teaching in the future.

Bonus Point for Over 65% Course

Evaluation Response Rate• The end of the evaluation period for this semester is Thursday

December 10 at 11:59PM.

• If, by the end of the course evaluation period, at least 65.00%

of the students enrolled in this course have completed the

course evaluations, then every student in the course will

have 1% bonus added to their final course mark.

• If fewer than 65.00% of students complete the course

evaluations by the deadline, then no bonus point will be

added for any student.

• Results so far (as of 3:15pm today):

• Invited: 940 students

• Responded: 252 students

• Response Rate: 26.81%

Last day I asked

A spring with a mass attached to it is stretched and

released. When the spring returns to equilibrium, is the

mass moving?

Answer: Yes! It is not accelerating, but it is moving at that

moment. Inertia then carries it past equilibrium to the other

side. After passing equilibrium, the acceleration is opposite

the velocity, so it slows down, eventually turning around.

Equilibrium is at x = 6 in this animation.

Some oscillations are not sinusoidal:

Period, frequency, angular frequency

• The oscillation frequency f is measured in cycles per

second, or Hertz.

• We may also define an angular frequency ω in radians per

second, to describe the oscillation.

• The time to complete one full cycle, or one oscillation, is

called the period, T.

• The frequency, f, is the number of cycles per second.

Frequency and period are related by

The Spring-Mass System

The force exerted on the mass by the spring:

F = −k x (Hooke’s Law)

F = m a (Newton’s Second Law)

xm

k

dt

xda

2

2Combine to form a

differential equation:

The Spring-Mass System

xm

k

dt

xda

2

2

kxFs

m

Fa Net

xm

kax

Simple Harmonic Motion

If the initial position of an object in SHM is not A, then we

may still use the cosine function, with a phase constant ϕ0

measured in radians.

In this case, the two primary kinematic equations of SHM

are:

Simple Harmonic

Motion (SHM)

)cos( 0 tAx

)sin( 0 tAdt

dxv

)cos( 0

2

2

2

tAdt

xd

dt

dva

This is the position graph of a

mass on a spring. What can

you say about the velocity

and the force at the instant

indicated by the dotted line?

A. Velocity is positive; force is zero.

B. Velocity is negative; force is zero.

C. Velocity is negative; force is to the right.

D. Velocity is zero; force is to the right.

E. Velocity is zero; force is to the left.

This is the position graph of a

mass on a spring. What can

you say about the velocity

and the force at the instant

indicated by the dotted line?

A. Velocity is positive; force is zero.

B. Velocity is negative; force is zero.

C. Velocity is negative; force is to the right.

D. Velocity is zero; force is to the right.

E. Velocity is zero; force is to the left.

What is ϕ0?

x Acos(t 0)

A. −π/3

B. +π/3

C. −2π/3

D. +2π/3

E. 0

S.H.M. notes.

• The frequency, f, is set by the properties of

the system. In the case of a mass m

attached to a spring of spring-constant k,

the frequency is always

• A and ϕ0 are set by the initial conditions: x0

(initial position) and v0 (initial velocity).

• A turns out to be related to the total energy

of the spring oscillator system: E = ½ k A2.

f 1

2

k

m

Which of the following quantities in the

description of simple harmonic motion is

not determined by the initial position and

velocity of the mass?

A. the amplitude, A

B. the phase constant, ϕ0

C. the angular frequency, ω

Clicker question

A mass is oscillating on a spring in S.H.M.

When it passes through its equilibrium point,

an external “kick” suddenly decreases its

speed, but then it continues to oscillate. As a

result of this slowing, the frequency of the

oscillation

A. goes up

B. goes down

C. stays the same

Vertical Mass on a Spring

Vertical Mass on a Spring

Before Class 21 on Monday

Please finish reading Chapter 13 on Oscillations.

Problem Set 9 on Chapters is due Tuesday Dec.1 at

11:59pm.

Something to think about over the weekend: If you double

the mass of a mass on a spring, how does this change the

frequency? If you double the mass of a swinging pendulum,

how does this change the frequency? What is the difference

here?