Devil physics The baddest class on campus Pre-DP Physics
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Transcript of Devil physics The baddest class on campus Pre-DP Physics
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