assn2 - 1.138J/2.062J/l8.376J WAVE PROPAGATION Fall 2006 l...

1.138J/2.062J/l8.376J, WAVE PROPAGATION
Fall.
2006
lIIT
C.
C. lIci
Hornc~vork no.
2
Gi~rcn Scp
26,2006.
Diic Oct,ohcr
5. 2006.
In all exercises, please describe the physical meaning of your mathematical
results. Use graphics if it can help the explanation. If you do any numerical
computations, feel free to use Matlab.
1.
Rcflcct,ion from a scrni-infinit,c rod. Consider t,llc lorlgitiidinal nravcs in
a
scmci-
irlfirlit,c clast,ic rod of llrliforrn cross scct,ion. The crltl at
rc;
=
0
is st,rcss-ficc. Tllcrc is no
cxt,crnal stress along t,hc rotl. The initial displaccrncnt arltl velocity arc
:
Find the dcflcctiorl in t,hc rotl for all tirrlc
t
>
0 by using the rrlct,llod of images
2.
Read
$1.
Chapter one. Xot,cs.
Consider an infinit,cly long st,ring taut ~vit,ll tcnsiorl
T ,
m <
.T
<
m
frcc from any
lat,cral slipport,.
-4
conccnt,ratcd mass
. \I
is at,t,acllcd t,o t,hc string at t,llc origin. Sho\v
first that Nc~vt,on's law for t,llc mass requires that
a a .
=
(H.2.1)
\I-\.'
d"
~ ( t )
T-T'L(O-,
t)
+
T-1 +(O+.