3.032 Problem Set 1 solutions
Fall 2006
ue: Start of lecture, 9 15 06
1. Thin-lm silicon nitride cantilevers such as the one shown in Figure 1 are used in
scanning probe microscopy, resonant frequency measurements, and electrostatic actuation. Let us appr
2014 2.71/2.710 Optics, Solution for HW3
1. Optical path length calculation using a thin lens
Figure 1.
a) The thin lens approximation can be applied to the lens makers equation as:
1
f
(n 1)
Using R1
1
R1
1
R2
(n 1)d
nR1R2
, we get:
R, R2
FFP is located
Massachusetts Institute of Technology
2.71/2.710 Optics
Solution for HW2
Spring 2014
1. Modified from Pedrotti 18-9
M
A B
C D
lens
d
d
f
d
f
EFL f eq
FFP p
PP r
D
D
C
C
f f
C
f
d
f
f
cm
cm BFP q
cm PP s
d
f
A
C
A
cm
C
cm
1
Massachusetts Institute of Techn
2.003 Engineering Dynamics
Problem Set 8-Solution
This was an optional homework handed out as a study aid in advance of the second
quiz in the course in the fall of 2011. It is an actual quiz from a prior year. There
were no concept questions. Students ha
2.003 Engineering Dynamics
Problem Set 7-Solution
Problem 1:
A cart of massM is connected to a dashpot with constant c. A force F(t) acts on the mass,
where the force is given by F (t ) Fo cos( t ) .
a). Use Lagranges equations to derive the equation(s) o
3.052NanomechanicsofMaterialsandBiomaterials
FinalExam:05.20.07
3.052 Nanomechanics of Materials and Biomaterials :
Spring 2007 Final Exam
1. Single Macromolecule Force Spectroscopy. (Data taken from: Oesterhelt, et al. New J.
Physics1(1999)6.16.11).Fig
2.710 Optics
Quiz 2 Solutions
Spring 09
1. Solution:
n
z
o
g1 (x, z) = a1 exp i2
sin + cos
,
6
6
n
x
o
z
g2 (x, z) = a2 exp i2
sin + cos
,
3
3
At z = 0,
x
a1 = 1
a2 =
x 1
x
1
2
p
3
2
I(x) = |g1 (x, 0) + g2 (x, 0)|2 = a1 ei2 2 + a2 e i2 2
"
p !#
2a1 a2
2.003 Engineering Dynamics
Problem Set 6 with concept question answers
Problem 1: A slender uniform rod of mass m2 is attached to a cart of mass m1 at a frictionless
pivot located at point A. The cart is connected to a fixed wall by a spring and a damper.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.710 Optics
QUIZ 2
Spring 09
Monday, April 27th , 2009
1. Interference Two plane waves of wavelength
are propagating on the xz
plane such that their electric elds at (x = 0, z = 0) reach simultaneously their
maximum