### Ch 14 slides

```Q13.1
An object on the end of a spring is oscillating in simple harmonic
motion. If the amplitude of oscillation is doubled, how does this
affect the oscillation period T and the object’s maximum speed vmax?
A. T and vmax both double.
B. T remains the same and vmax doubles.
C. T and vmax both remain the same.
D. T doubles and vmax remains the same.
E. T remains the same and vmax increases by a factor of
2.
A13.1
An object on the end of a spring is oscillating in simple harmonic
motion. If the amplitude of oscillation is doubled, how does this
affect the oscillation period T and the object’s maximum speed vmax?
A. T and vmax both double.
B. T remains the same and vmax doubles.
C. T and vmax both remain the same.
D. T doubles and vmax remains the same.
E. T remains the same and vmax increases by a factor of
2.
Phase angle
Draw x(t) for a simple harmonic oscillator with A =
2m, T = 4s and the following three phase
angles: f0 = 0, p/2, -p/2. Draw circular motion
diagram to show initial conditions. Calculate
the value of x(0) in the three situations to make
Q13.2
This is an x-t graph for
an object in simple
harmonic motion.
At which of the following times does the object have the most
negative velocity vx?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
A13.2
This is an x-t graph for
an object in simple
harmonic motion.
At which of the following times does the object have the most
negative velocity vx?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
Q13.3
This is an x-t graph for
an object in simple
harmonic motion.
At which of the following times does the object have the most
negative acceleration ax?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
A13.3
This is an x-t graph for
an object in simple
harmonic motion.
At which of the following times does the object have the most
negative acceleration ax?
A. t = T/4
B. t = T/2
C. t = 3T/4
D. t = T
SHO equations
• A simple harmonic oscillator has an amplitude of 2 m and
oscillates with a period of 2s. What is its maximum velocity?
• The SHO is started with a phase angle of f = p/2 with the same
period and amplitude. Draw the position vs. time graph.
• The same SHO starts moving in the positive x direction starting
at x = 1m at t = 0s. What is the phase angle for this situation?
Energy in SHM
• Energy is conserved during SHM and the forms (potential and
kinetic) interconvert as the position of the object in motion
changes.
Energy in SHM II
• Energy converts between kinetic and potential energy.
Q13.7
This is an x-t graph for
an object connected to
a spring and moving in
simple harmonic
motion.
At which of the following times is the kinetic energy of
the object the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. more than one of the above
A13.7
This is an x-t graph for
an object connected to
a spring and moving in
simple harmonic
motion.
At which of the following times is the kinetic energy of
the object the greatest?
A. t = T/8
B. t = T/4
C. t = 3T/8
D. t = T/2
E. more than one of the above
Find velocity
1) What is the velocity as a
function of the position v(x) for a
SHO glider with mass m and
spring constant k?
Use conservation of energy
2) What is the maximum velocity
of the glider? Compare this max
velocity to your previous result to
find w for a mass on a spring.
Vibrations of molecules
• Two atoms separated by their internuclear distance r can be
pondered as two balls on a spring. The potential energy of such a
model is constructed many different ways. The Leonard–Jones
potential shown as Equation 13.25 is sketched in Figure 13.20
below. The atoms on a molecule vibrate as shown in Example
13.7.
Old car
The shock absorbers in my 1989 Mazda with mass 1000 kg are
completely worn out (true). When a 980-N person climbs slowly
into the car, the car sinks 2.8 cm. When the car with the person
aboard hits a bump, the car starts oscillating in SHM. Find the
period and frequency of oscillation.
How big of a bump (amplitude of oscillation) before you fly up out
Damped oscillations II
Forced (driven) oscillations and resonance
• A force applied “in synch” with a motion already in progress
will resonate and add energy to the oscillation (refer to Figure
13.28).
• A singer can shatter a glass with a pure tone in tune with the
natural “ring” of a thin wine glass.