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Unformatted text preview: Chapter 15 P15.26 The angle of the crank pin is θ = ωt .
Its x-coordinate is ω
Piston x = A cos θ = A cos ωt A where A is the distance from the
center of the wheel to the crank pin.
This is of the form x = A cos ωt + φ ,
so the yoke and piston rod move
with simple harmonic motion. b Section 15.5
P15.27 (a) g FIG. P15.26 The Pendulum
T = 2π
L= (b) x = –A gT 2
4π 2 L
g e9.80 m s ja12.0 sf
2 = Tmoon = 2π 4π 2
L = 2π g moon 2 = 35.7 m 35.7 m
1.67 m s 2 = 29.1 s TT = 2π LT
gT TC = 2π LC
gC We know TT = TC = 2.00 s For which, we see LT LC
gT gC or P15.29 The period in Tokyo is
and the period in Cambridge is P15.28 g C LC 0.994 2
= 1.001 5
g T LT 0.992 7 The swinging box is a physical pendulum with period T = 2π I
mgd The moment of inertia is given approximately by
mL2 (treating the box as a rod suspended from one end).
3 Then, with L ≈ 1.0 m and d ≈ T ≈ 2π 1
2 mL2 mg ch
2 = 2π a f 2 1.0 m
= 1.6 s or T ~ 10 0 s .
3 9.8 m s e j x ( t) 449 ...
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
- Fall '11