Unformatted text preview: scillator 12ghlustgated in Figures
as il
r
15.21 and 15.22. Assume the mass is 375 g, the spring
constant to ﬁnd xN/m,thatd is a maximum,swhich(a) How
0.100 N /m. means dT/dx = 0. Noting that dT/dx = −dT/dh,
We wish is 100 such an T b
long does it takes for the amplitude to drop to half its
initial value? (b) What If? How long doesdT take dTr the
it
fo
=−
=0
(8)
mechanical energy to drop to half its dx itial dh lue?
in
va (c) Show that, in general, the fraction2 l rate at which the
1a
l + h2
d
12armoni oscillator is
amplitude decreases in a damped h
c =0
2π
(9)
dh
gh
half the fractional rate at which the mechanical energy
−1/2
decreases.
12
2
1
−l2
1
12 l + h
2o
(10)
71. A block π f mass m is c2 +
onnected to two springs o=f0
f orce con2
12gh
g
gh
stants k 1 and k 2 as shown in Figures P15.71a and P15.71b.
−l2
1
In each case, the block moves=⇒ a frictionless t= 0 after it
on
+ able
(11)
2
12gh
is displaced from equilibrium and released. g how that in
S
the two cases the block exhibits simple h12h2 = l2 motion
armo...
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 Fall '08
 StanJones
 Physics, Force, Mass, Simple Harmonic Motion, Work, pivot point

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