Oscillationsand SimpleHarmonic Motion
Problemi
(a)A springstretches
by 0.015m whena 1.75kg objectis suspended
fromits end.How
muchmassshouldbeattached
to thespringsothatits frequency
of vibrationis/= l.Q fl2r
I try = rtt4) = D
tl
ll
l'.
ft
It
mg
X = O . Dl E r . r
K = (r-rsh) (z.r*15,)_ l,lqx ld>,n
(o.orBm)
n
-)'^,
+=
F- ---)4 -rr,9'':
m= t.75 K?
:'-:-'
17-
, ra = ( l.tr " lo=N/D
ro: frln*g*
qw
l(x-."9 =O --) K=nYY
:@
4 -t* (:.o *a)'
j1r6 ;
a,:*^a.;2.e.,t Sou,-""t
-"v*J W JryrbE"lu
o5 Noe""'a -Q-c.t
. . . ^ 1 " |a++)j;-fub,L
**--|vU
o8
sHrD.
(b) An oscillatingblock-springsystemhasa mechanicalenergyof 1.00J, an amplitudeof
10.0cm, and a maximumspeedof 1.20m/s. Find the springconstant,the massof the
block, andthe frequencyof oscillation.
-*"K'4 o8 "- 9>ea<9"Ji* Jctd-a
T*
W:
=
/" n'!^bJ ^t Ac"'J v,., '
,1ry*".9_--t.3ltr?vrr
E = l"oD{
A
= \o"Dcrcl
= D.\D n
V- = l,]o,'r/s
l\= ?
E'
,/x,"nvr.i
E =
( o.or"" tA""r X =o )"PE=o)
F=r/aKAa
( O.-.^,*
'l^)(A* ->
rD= ?
t=3
E=
/'
r[ r,lV*r-+
\
r-1
=
rn = 3+
|'
Z\lr
=O )
V =O ,4t' KE
)
K=12
*
"('.""1)
(o.to'"')
A*
K=)ooly^
- ] t r'oo5-) =';
V."
\-=ellL
-rlr
I
arT I
u,:qn
( aooNfr")
I ^q l(a
(l.to"/e )"
+= ["qlHz
Problem 2
A 0.45kg massis attachedto a springwith a force constantof26.0 N/m andreleasedfrom
resta disianceof 3.25 cm from the equilibrium position ofthe spring.(a) What is the period
of the mass?(b) Use conservationof enerry to find the speedof the masswhen it is halfinay
to the equilibrium position.(c) What is the maximumspeedof the mass?(d) What is the
magnitudeof the maximumaccelerationof the mass?
I
N)= O"95KX
l(
l-
--
).to"oN/r.r
-l
=
/1= a.A5ceq O.o3a5 r')
l-""__!,-^s_A4_*4__f
%
le---------+l
5. J. b crr)
,n e- i )r{fr ,Wp;A
4=z'
(") T=,/+= XrPr
|
(b)
-
d\ rl
.o"ttSYX
I to.oN/ro
m=o.r/5r+
K = )-G,oN/'n
A=O.b315o
X = O , o l t " a . Sr " )
V: ?
+\AryewA ""c
a'.'72;fo^)"
ad Y\,
tn;ry'&tf
a6
lT-= O,C3s I
,,
/1KAo= Tamv\ TxKx^
.bfct (n'-x')
l/^^.rt = 7+K (A*-*^) ---- V = J!*
E=
(rr"oN/^)
V = /
[co.ozas^1.-16.orr,re-)']
I o.r stzg
.,
V = o,I\.r/s
(.)
f
= t/xKA'= 7aD V-t -----+ Vm =
=
Jt"o
V.q = O").5 -/s
(J)
o.=ftr^,r= Aly^
Om=l,lnfs^
( o"oaes^)