1. The document discusses kinematics and energy in simple harmonic motion. It considers a dot moving in uniform circular motion around a bicycle wheel. 2. It asks which position on a graph of position vs. time has the maximum velocity for the dot. The answer is the equilibrium position (0) because the velocity of a simple harmonic oscillator is greatest at this point according to the equation for velocity and unit circle concept. 3. It also asks which position has the maximum acceleration, explaining that according to Newton's Laws and the restoring force equation (F=-kx), acceleration is greatest when the displacement and restoring force are greatest, which is at the maximum displacement positions.

1. Images takenfromProf. Bates’ andRottler’s Section202 Lecture notes and NelsonPhysics for Scientists andEngineers, An Interactive ApproachCustomVolume 1
PHYS 101 LO1
Kinematics and Energy in Simple Harmonic Motion
Question1a: Consideradot on a bicycle wheel rotatinginuniformcircularmotion.The dotundergoes
simple harmonicmotionasitmovesaround.Giventhe followinggraphof the dot’sposition vs.time,
whichof the followinglabelsrepresentsthe positionatwhichthe magnitude of the dot’svelocityisatits
maximum?(circle one)
A) A B) B C) C D) D E) E
1b) Explain your answer usingunit circlesand the equationfor velocityof a simple harmonic
oscillator.
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1c) Explain your answer usingConservationof Energy.
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1d) Explain your answer usingrestoring forcesand simple harmonic motion.
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Question2: Whichof the labelsrepresentsthe positionatwhichthe magnitude of the dot’sacceleration
isat itsmaximum? (circle one)
A) A B) B C) C D) D E) E
Explainusing restoringforces and Newton’sLaws.
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A
B
C
D
E

2. Images takenfromProf. Bates’ and Rottler’s Section202 Lecture notes and NelsonPhysics for Scientists andEngineers, An Interactive ApproachCustomVolume 1
PHYS 101 LO1
Kinematics and Energy in Simple Harmonic Motion
Question1a: Consideradot on a bicycle wheel rotatinginuniformcircularmotion. Whenviewedon
fromabove,the dot can be seen undergoingsimple harmonicmotionasitmovesaround.Giventhe
followinggraphof the dot’spositionvs.time,whichof the followinglabelsrepresentsthe positionat
whichthe magnitude of the dot’svelocityisatitsmaximum?
A) A B) B C) C D) D E) E
1b) Explainyour answerusing unit circlesand the equationfor velocityofa simple harmonicoscillator.
The velocityof a simple harmonicoscillatorisknowntobe . Asit isa
sine function, using the unit circle, we know that the largest value of a sine functionoccurs at 𝜋/2 and
3𝜋/2. Imagining the bike wheel as a unit circle then, its largest velocity is when the dot is at the top or
the bottom of the wheel, in other words, when it is at the equilibrium position x=0.
1c) Explain your answer using Conservation of Energy.
When the dot is at its maximum displacement (x= +/- 0.5m), it’s in a sense momentarily “not
moving”,andall of itsenergyiscontainedaspotential energy.Whenitstartsmovingbackto equilibrium
due to the restoring forces on it, its velocity increases and it loses its potential energy as displacement
decreases. Once at equilibrium, all its potential energy has been converted into kinetic energy (KE =
1/2mv2
), so velocity is at its maximum.
1d) Explain your answer using restoring forces and simple harmonic motion.
Similarly to the previous explanation, when the dots is at its maximum displacement, it’s like a
springthat hasbeenpulledandistemporarilyatrest.The restoringforce onthe dot (F= -kx) pullsitback
towards the equilibrium position (the top/bottom of the circle). At equilibrium, its velocity will be at its
maximumbefore itgoespastequilibrium againandvelocitydecreasesasthe restoringforce acts against
it, tyring to pull it back to equilibrium.
Question2: Whichof the labelsrepresentsthe positionatwhichthe magnitude of the dot’sacceleration
is at its maximum?
A) A B) B C) C D) D E) E
A
B
C
D
E

3. Explain using restoring forces and Newton’s Laws.
According to Newton’s Laws, if an object has a net force acting on it, it must be accelerating. In
thiscase,we knowthatthere isanetrestoringforce onthe dotinthe formof Hooke’sLaw (F= -kx) sowe
knowthat it accelerates andmustfollow the equationF=ma.The restoringforce islargestwhenthe dot
has moved its maximum displacement, therefore the acceleration is largest when the dot is at its
maximum displacement, or endpoints of its motion.