Solution pts Spring STAT B Take Home Due T In class Name Updated email protected NOTES

Solution pts Spring STAT B Take Home Due T In class Name

B Take Home Due T In class Name Updated email protected NOTES i All work except code

Solution pts Spring STAT B Take Home Due T In

class Name Updated email protected NOTES i All work except code

Solution pts Spring STAT B Take Home Due

Solution pts Spring STAT

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Paper instructions

Need help ans. these questions. (looks like matlab is invovled with is killing me) see attachement.1
(100+5pts) Spring 2016
STAT 305B (Take-Home)
Due 3/29 (T In class
) Name_______________________
(
Updated 3/[email protected]
)
NOTES
: (i) All work (except
code) associated with a given part MUST be placed DIRECTLY beneath that part
(ii) Begin each problem on a new page.
Problem 1 (25+5pts)
In this problem you will analyze the uncertainty claims made by physics Professor Walter Lewin in
https://www.youtube.com/watch?v=4a0FbQdH3dY
in relation to the measured period of a swinging pendulum. [This
topic begins @ ~ 2 minutes into the video.]
By the term ‘uncertainty’ we will assume it is a
2? uncertainty.
(a)(4pts)
Let
L=the act of measuring the length of the pendulum.
Assume
)
,
(
~
L
L
N
L
?
?
. (i)Give the numerical values
for
L
?
and
L
?
. Then (ii) verify Professor Lewin’s claim that the percent uncertainty is ~1%.
Solution
:
(b)(4pts)
To mathematically compute
L
?
and
L
?
is very
difficult. Use 10
6
simulations to obtain their values.
Solution
: [See my code @ 1(b)]
(c)(6pts)
Professor Lewin claims that because the percent uncertainty in
L
is ~1%, the resulting uncertainty in calculating
the pendulum period
L
g
T
)
/
2
(
?
?
is only ~0.5%. Use your answers in (a) to arrive at (i)
T
?
, (ii)
T
?
, and (iii) to
verify his claim re: percent uncertainty. [Do
not
use simulations of
T.
You should be able to compute these directly.]
Solution
:
(d)(6pts)
Professor Lewin points out that the uncertainty in the calculation
of
T
must be followed by a recognition that
one must then measure
T
as the pendulum swings. Let
Q
denote the measurment error associated with the stop time after
any chosen number of pendulum swings.
. Assume this error is independent of
T.
Let
Q
mT
W
?
?
denote the act of
measuring
m
periods of the pendulum swing prior to stopping. The period estimator is then:
m
Q
T
m
W
T
/
/
?
?
?
?
. Arrive
at the expression for
T
?
?
as a function of only
m
. [Note: Assume
)
,
0
(
~
Q
N
Q
?
. You should be able to identify the
numerical value for
Q
?
.]
Solution
:
(e)(5pts)
Professor Lewin claims that by counting
10
?
m
periods, the resulting uncertainty in relation to
T
?
is 0.02 sec.
(i) Use your expression in (d) to show that his claim is incorrect, and then (ii) explain why he ‘messed up’.
Solution
:

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