Transcript Ch13-2 Simple Harmonic Motion

Chapter 13: Oscillations About Equilibrium
Whenever F = -kx or U(x) is a parabola
F = -kx
U = kx2/2
Chapter 13: Oscillations About Equilibrium
Ch13-1 Periodic Motion
T = period – the time for one cycle or repeat time
f = frequency – the number of cycles per second
f = 1/T
 = angular frequency – radians per second
 = 2f = 2/T
Don’t confuse angular frequency with
angular velocity.
Chapter 13: Oscillations About Equilibrium
Ch13-2 Simple Harmonic Motion (SHM)
Chapter 13: Oscillations About Equilibrium
Ch13-2 Simple Harmonic Motion (SHM)
Displaying Position Versus Time for Simple Harmonic Motion
x = Acos(2t/T)
t=0
Chapter 13: Oscillations About Equilibrium
Ch13-2 Simple Harmonic Motion (SHM)
Simple Harmonic Motion as a Sine or a Cosine
Chapter 13: Oscillations About Equilibrium
Ch13-2 Simple Harmonic Motion (SHM)
P13.8 (p.425)
CT1: A mass attached to a spring oscillates back and forth as
indicated in the position vs. time plot below. At point P, the
mass has
A. positive velocity and positive acceleration.
B. positive velocity and negative acceleration.
C. positive velocity and zero acceleration.
D. negative velocity and positive acceleration.
E. negative velocity and negative acceleration.
F. negative velocity and zero acceleration.
G. zero velocity but is accelerating (positively or negatively).
H. zero velocity and zero acceleration.
CT2: A mass suspended from a spring is oscillating up and
down as indicated. Consider two possibilities: (i) at some
point during the oscillation the mass has zero velocity but
is accelerating (positively or negatively); (ii) at some
point during the oscillation the mass has zero velocity
and zero acceleration.
A. Both occur sometime during the oscillation.
B. Neither occurs during the oscillation.
C. Only (i) occurs.
D. Only (ii) occurs.
Chapter 13: Oscillations About Equilibrium
Ch13-3 Connections Between Uniform Circular
Motion and SHM
Chapter 13: Oscillations About Equilibrium
Ch13-3 Connections Between Uniform Circular
Motion and SHM
Position Versus Time in Simple Harmonic Motion
Chapter 13: Oscillations About Equilibrium
Ch13-3 Connections Between Uniform Circular
Motion and SHM
Velocity Versus Time in Simple Harmonic Motion
Chapter 13: Oscillations About Equilibrium
Ch13-3 Connections Between Uniform Circular
Motion and SHM
Acceleration Versus Time in Simple Harmonic Motion
Chapter 13: Oscillations About Equilibrium
Ch13-3 Connections Between Uniform Circular
Motion and SHM
P13.22 (p.425)
P13.66 (p.428)
Chapter 13: Oscillations About Equilibrium
Ch13-4 The Period of a Mass on a Spring
P13.63 (p.427)
P13.31 (p.426)
k
m1
Factors Affecting the Motion of a Mass on a Spring
Chapter 13: Oscillations About Equilibrium
Ch13-5 Energy Conservation in Oscillatory Motion
E = mv2/2 + kx2/2 = kA2/2 = mvmax2/2 = mA22/2
Chapter 13: Oscillations About Equilibrium
Ch13-5 Energy Conservation in Oscillatory Motion
U = kA2cos2t/2
K = mA22sin2t/2 = kA2sin2t/2
Chapter 13: Oscillations About Equilibrium
Ch13-5 Energy Conservation in Oscillatory Motion
P13.67 (p.428)
CT3: In P13.67b, which principle do we have to
use to get the speed of the bob and bullet right
after the collision?
A. Newton’s laws.
B. Conservation of energy.
C. Conservation of momentum.
D. The work-kinetic energy theorem.
CT4: In P12.67b, which principle do we have to
use to get the speed of the bullet from the
height the bob rises?
A. Newton’s laws.
B. Conservation of energy.
C. Conservation of momentum.
D. The work-kinetic energy theorem.
Chapter 13: Oscillations About Equilibrium
Ch13-6 Simple Pendulum
r
t
Chapter 13: Oscillations About Equilibrium
Ch13-6 Simple Pendulum
P13.67c (p.428)
CT5: In P13.52a the acceleration of gravity at the
surface of the Moon is one-sixth that at the
surface of the Earth. If the pendulum were taken
to the Moon, the period will
A. increase.
B. decrease.
C. stay the same.
Simple Pendulum:
Energy View
Chapter 13: Oscillations About Equilibrium
Ch13-7 Damped Oscillations
Chapter 13: Oscillations About Equilibrium
Ch13-7 Damped Oscillations
Chapter 13: Oscillations About Equilibrium
Ch13-8 Driven Oscillations and Resonance