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k1 .: 481n—1 mH.= lamu m0 := 35.53mu
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mH+ a) Here are my functions, one with a ﬁxed k, the other sol can vary k. 1 2
Vx:=—kx
() 2] 1 2
v(x,k :2 —kx
) 2 510—” 0 510—11 As l increase the value for k, the potential gets steeper. That is, the curvature increases. This
is easily understood by noting that the curvature (our deﬁnition,_ the second derivative) is always going to be twioe the value of k. b) We know from lecture the following relations: x(t) := A sin(m 't) 13:: —kA E2: 610_ 2OJ A2: 2Ek1 A=7.597x 10‘ 9N 2 PSI C? a) :: — co = 5.457 x 1014Hz x(t) :2 Asin(u)~t)
H1 ‘
110—8
5109
x(t) 0
~510_9
*1 “10—8  ~ 4 ‘14 ‘14
0 110 ‘4 210 ‘ 310 410 t c) The period is one over the frequency, but we have to take (0 out of radians 1 .. w:l v=8.686x 1013112 T:=— T=1.151X10 143 27: v
or, converting this to a Unit we think about freq uentiy, the femtosecond
f5? 10— 15s
1 =11.513fs . “I
1(k) 2: 21: —— k T(1.1k1)=10.977f3 101.9111) = 12.136 fs t(11) 2: 21: £ iii (3;) 1(11111) = 12.075 fs 1(0.9p1) = 10.952fs When the spring constant is increased, it pulls harder on the attached mass (as pictured in
the reduced mass sense). Therefore, it makes sense that it would turn the mass around faster, giving it a shorter period. When the mass is increased, it's harder to reverse the
momentum, giving it a longer period. ' 2 2 I 3
WY) 3: Ekl')’ —yy 1
:2 _.k .
30/) 2 1 y The graph is now skewed to the positive, but still has an overall parabolic nature (at least
over ther range shown) that is a little stretched out. One might guess that the wider potential would give lower frequencies of oscillation as compared to the harmonic
potential. 4? A lmwsyv3w/ IMZIO’C’M / C=2'7782<108M5J, hré'éllxlb’}?u.§ ﬁ;él.8ﬂ/WV .
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 Fall '08
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