Chapter 36
Diffraction
Physics 72 Bareza AY 1516 1st sem
1
Diffraction interference effects due to combining many light waves
the bending of light around an obstacle
Diffraction is interference.
Physics 72 Bareza AY 1516 1st sem
2
Screen
Obstacle
Poin
NATIONAL INSTITUTE OF PHYSICS
U.P. DILIMAN CAMPUS
PROBLEM SET NO. 7 (Capacitor and Dielectric)
Date Due : 29 September 2015 (Tuesday)
1.
Two parallelplate capacitors, each with a capacitance C1 = C2 = 2 F, are connected
in parallel across a 12V battery.
EEE 33 Homework 2
Due: 27 August 2015
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5. Find the effective inductance seen at terminals ab.
Problem 6
Problem 7
Chapter 34
Geometric Optics
Physics 72 Bareza AY 1516 1st sem
1
Chapter 34
Geometric Optics
341 Reflection and Refraction at a Plane Surface
342 Reflection at a Spherical Surface
343 Refraction at a Spherical Surface
344 Thin Lens
Physics 72 Bare
EEE 33 Homework 6
Due 30 September 2015
Problem 1 (treat the two items as one problem)
Problem 2
Problem 3
Write the form of the solution to the following differential equations:
a.
b.
d4 v
d3 v
d2 v
dv
+7
+33
+97 +102 v=0
4
3
2
dt
dt
dt
dt
6
5
4
d i
d i
NATIONAL INSTITUTE OF PHYSICS
U.P. DILIMAN CAMPUS
PROBLEM SET NO. 2 (Electric Force and Electric Field)
Date Due : 18 August 2015 (Tuesday)
1.
An insulating rod of length L has charge q
uniformly distributed along its length.
A ) What is the linear charge
EEE 33 Homework 4
Due 10 September 2015
Problem 1
Problem 2
Problem 3. Find v(t) for t < 0 and t > 0.
Problem 4. Find i(t) for t < 0 and t > 0.
Problem 5
Problem 6. In pro
#11
1.76
! 10of
m."
Determine
a time
1.6
10#2 s? the kinetic energy of the electron.
* 24.
unstrained
spring has
a length
0.32
m and a
* 48. AnThe
drawinghorizontal
shows a positive
point
chargeof!q
1, a second point
m mmh Two tiny spheres have the same m
Chapter 35
Study this chapter then answer the uploaded
Recit 17 in UVLE. Print a copy and encircle the
letter of the best answer.
Submission due: Nov 26 (Thurs)
Nov 26 (Thurs): Inclass recit 18
(Topic: Diffraction)
Physics 72 Bareza AY 1516 1st sem
1
NATIONAL INSTITUTE OF PHYSICS
U.P. DILIMAN CAMPUS
PROBLEM SET NO. 3 (Gauss Law)
Date Due : 01 September 2015 (Tuesday)
1.
The electric field components in the Figure are Ex = 0, Ey =
by1/2 (b = 8830 N/Cm1/2) and Ez = 0. Find :
A ) the electric flux throu
EEE 33 Homework 3
Due 3 September 2015, 5 PM
Problem 1
Problem 2
Write the mesh equations for the following circuit:
Problem 3
Write the nodal equations for the following circuit:
EEE 33 Homework 5
Due: 23 September, 5 PM
Problem 1
Problem 2
The height of the waveform is 1. Assume that the waveform value prior to t = 2 is 1.
Problem 3
Assume that the form of the steadystate response is K exp(2t).
Problem 4
Problem 5
Problem 6
Pr
Strength of Materials
Prof S. K. Bhattacharya
Department of Civil Engineering
Indian Institute of Technology, Kharagpur
Lecture  9
Analysis of Strain  III
(Refer Slide Time: 00:48)
Welcome to the 3rd lesson on module 2 on analysis of strain.
(Refer Slid
Chapter 5
Direct Current
Machines
Artemio P. Magabo
Professor of Electrical Engineering
with revision Aug 2012 (J.Orillaza
J.Orillaza)
Department of Electrical and Electronics Engineering
University of the Philippines  Diliman
Features of a DC Machine
q
Chapter 2
Basic Navigational Mathematics,
Reference Frames and the Earths
Geometry
Navigation algorithms involve various coordinate frames and the transformation of
coordinates between them. For example, inertial sensors measure motion with
respect to an
3.3
Laser Threshold
3.2
Given:
(
)
(
)
(
)
,
, express P and D in terms of E, and thereby derive a first order
a) Assuming
equation for the evolution of E.
Solution:
(
)
(eq. 1)
(
)
(eq. 2)
Substituting eq. 1 into eq. 2, and solving for D,
(eq. 3)
Subst
3.5.2 Do the linear stability analysis for all the fixed points for Equation (3.5.7), and confirm that
Figure3.5.6 is correct.
Equation 3.5.7 is
Where
For
The only fixed point is
So,
For
is stable
The fixed points are
and
So,
(
)
is unstable
is stable
3
3.2. For each of the following exercises, sketch all the qualitatively different vector fields that occur as r
is varied. Show that a transcritical bifurcation occurs at a critical value of r, to be determined. Finally,
sketch the bifurcation diagram of f
Solving Equations on the Computer:
2.8.2 Sketch the slope field for the following differential equations. Then "integrate" the equation
manually by drawing trajectories that are everywhere parallel to the local slope.
a) =
b) = 1 2
c) = 1 4(1 )
d) = sin
2.2 Fixed Points and Stability
Analyze the following equations graphically. In each case, sketch the vector field on the real line, find all
the fixed points, classify their stability, and sketch the graph of x(t) for different initial conditions. Then
tr
Exercise 2.6
2.6.1
Impossibility of Oscillation
Explain this paradox: a simple harmonic oscillation
is a system that oscillates in one
dimension (along the xaxis). But the text says that onedimensional systems cannot oscillate.
Solution:
The equation
is
2.3
Solve
Population Growth
(
) analytically for an arbitrary initial condition
.
a) Separate variables and integrate using partial fractions.
Solution:
(
)
(
(
)
)
Therefore,


(
)
At t = 0, N(0) = N0. Solving for C,
(
)
Solving for N,
( (
)
( (
)
(
)
Exercise 2.1
A Geometric Way of Thinking
In the next three exercises, interpret
2.1
as a flow on the line.
Find all the fixed points on the flow.
Solution:
Fixed points:
x = n where n
2.1.2
At which points x does the flow have greatest velocity to the r
Egye 332 probset 2
4.1.2 For each of following vector fields, find and classify all the fixed points, and sketch the
phase portrait on the circle
Fixed points:
Stability check:
= 1.73, stable point
= 1.73, unstable point
4.1.8
a)
, hence, for every poin
5.3.6 (Romeo the robot) Nothing could ever change the way Romeo feels about Juliet = 0 , = +
. Does Juliet end up loving him or hating him?
In matrix form:
=[
0
0
]
= 0 0 = [ ]
0
= = [ ]
1
There exists a line attractor along 0 . R stays constant.
b
a
b
4.5.3 (Excitable systems) Suppose you stimulate a neuron by injecting it with a pulse of current. If the
stimulus is small, nothing dramatic happens: the neuron increases its membrane potential slightly, and
then relaxes back to its resting potential. How
4.3.9 (Alternative derivation of scaling law) For systems close to a saddlenode bifurcation, the scaling
1
law Tbottleneck ~ ( 2 ) can also be derived as follows.
a) Suppose that x has a characteristic scale ( ), where a is unknown for now. Then = ,
wher
4.3.6 Draw the phase portrait as function of the control parameter . Classify the bifurcations that occur
as varies, and find all the bifurcation values of .
= + sin + cos 2
= + sin + cos 2 = + sin + 1 2 sin2
For   < 2, fixed points satisfy:
sin =
1