introductory video: simple harmonic motion simple harmonic motion

DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSPRE-DP PHYSICS

LSN 11-1: SIMPLE HARMONIC MOTIONLSN 11-2: ENERGY IN THE SIMPLE

HARMONIC OSCILLATORLSN 11-3: PERIOD AND THE SINUSOIDAL

NATURE OF SHM

Introductory Video:Simple Harmonic Motion

Objectives Know the requirements for simple

harmonic motion (SHM). Know the terms equilibrium position,

displacement, amplitude, period, and frequency. Be able to determine the values for these terms from a graph.

Calculate elastic potential energy from displacement and spring constant.

Calculate kinetic energy and velocity of an oscillating object using conservation of mechanical energy.

Objectives Understand the relationship

between the unit circle and SHM and how the two of them relate to the sinusoidal nature of SHM.

Know the meaning of angular velocity (ω) and how to compute it.

Use angular velocity and amplitude to compute position, velocity, and acceleration.

Oscillation vs. Simple Harmonic Motion An oscillation is any motion in which

the displacement of a particle from a fixed point keeps changing direction and there is a periodicity in the motion i.e. the motion repeats in some way.

In simple harmonic motion, the displacement from an equilibrium position and the force/acceleration are proportional and opposite to each other.

Simple Harmonic Motion: Spring

Definitions

Understand the terms displacement, amplitude and period displacement (x) – distance from

the equilibrium or zero point amplitude (A) – maximum

displacement from the equilibrium or zero point

period (T) – time it takes to complete one oscillation and return to starting point

Definitions

Definitions

Understand the terms period and frequency frequency (f) – How many

oscillations are completed in one second, equal to the inverse of the period

period (T) – Time for one complete oscillationf

T 1

Tf 1

Simple Harmonic Motion

In simple harmonic motion, the displacement from an equilibrium position and the force/acceleration are proportional and opposite to each other.

Simple Harmonic Motion: Spring The spring possesses an intrinsic

restoring force that attempts to bring the object back to equilibrium:

This is Hooke’s Law k is the spring constant (kg/s2) The negative sign is because the force

acts in the direction opposite to the displacement -- restoring force

kxF

Simple Harmonic Motion: Spring Meanwhile, the inertia of the

mass executes a force opposing the spring, F=ma: spring executing force on mass

mass executing force on spring

kxF

maF

Simple Harmonic Motion: Spring Elastic Potential Energy:

Kinetic Energy:

221 kxPE

221 mvKE

Simple Harmonic Motion: Spring Conservation of Energy:

22

22

21

21 21212121 mvkxmvkx

222

21

21

21 kAmvkx

Simple Harmonic Motion

Understand that in simple harmonic motion there is continuous transformation of energy from kinetic energy into elastic potential energy and vice versa

Simple Harmonic Motion: Spring

00 KEPEETotal

021 2 kxETotal

22 2121 mvkxETotal

2210 mvETotal

021 2 kxETotal

Simple Harmonic Motion: Spring

no displ, no energy, no accl

max displ, max PE, max accl, zero KE

half max displ, half max PE, half max accl, half max KE

zero displ, zero PE, zero accl, max KE

max displ, max PE, max accl, zero KE

Simple Harmonic Motion: Spring These forces remain in balance

throughout the motion:

The relationship between acceleration and displacement is thus,

kxma

xmka

Simple Harmonic Motion: Spring

Satisfies the requirement for SHM that displacement from an equilibrium position and the force/acceleration are proportional and opposite to each other

xmka

Relating SHM to Motion Around A Circle

Velocity

AfTAv

Trv

rCtdv

22

22

0

0

Period

km

vA

mvkA

vAT

TAv

0

20

2

0

0

2121

2

2

Period

kmT

km

vA

vAT

2

2

0

0

Frequency

mkf

Tf

kmT

21

1

2

Radians One radian is

defined as the angle subtended by an arc whose length is equal to the radius

1

rlrl

Radians

radnceCircumfererlrl

rnceCircumfere

22

2

Angular Velocity

fT

Trv

222360

20

Position

TtAx

ftAxtAx

Ax

2cos

2coscoscos

Velocity

Ttvv

ftvvtvv

vv

2sin

2sinsinsin

0

0

0

0

Acceleration

Ttaa

ftaa

Amka

xmka

2cos

2cos

0

0

0

Relating SHM to Motion Around A Circle These equations yield the following

graphs

Relating SHM to Motion Around A Circle These equations yield the following

graphs

Relating SHM to Motion Around A Circle These equations yield the following

graphs

Relating SHM to Motion Around A Circle These equations yield the following

graphs

Relating SHM to Motion Around A Circle These equations yield the following

graphs

Relating cos to sin

TtAx

ftAx2cos

2cos

TtAx

ftAx2sin

2sin

Definitions

Understand the terms displacement, amplitude and period displacement (x) – distance from

the equilibrium or zero point amplitude (A) – maximum

displacement from the equilibrium or zero point

period (T) – time it takes to complete one oscillation and return to starting point

Definitions

Objectives Know the requirements for simple

harmonic motion (SHM). Know the terms equilibrium position,

displacement, amplitude, period, and frequency. Be able to determine the values for these terms from a graph.

Calculate elastic potential energy from displacement and spring constant.

Calculate kinetic energy and velocity of an oscillating object using conservation of mechanical energy.

Objectives Understand the relationship between

the unit circle and SHM and how the two of them relate to the sinusoidal nature of SHM.

Know the meaning of angular velocity (ω) and how to compute it.

Use the relationship between the unit circle and SHM to compute position, velocity, and acceleration.

QUESTIONS?

#1 - 12 Homework