Chapter 13 Solutions - Mosinee School District

Chapter 13
Amin A1 A 2 0.10 m
13.62 We are given that x Acos( t) (0.25 m)cos(0.4 t ) .
(a) By inspection, the amplitude is seen to be A 0.25 m
(b) The angular frequency is 0.4 rad s . But km, so the spring constant is
k m
2
(0.30 kg)(0.4 rad s)
2
0.47 N m
(c)
Note: Your calculator must be in radians mode for part (c).
At t = 0.30 s, x 0.25 m cos 0.4 rad s 0.30 s 0.23 m
(d) From conservation of mechanical energy, the speed at displacement x is given by v A2 x
2
. Thus, at t
= 0.30 s, when x = 0.23 m, the speed is
v
0.4 rad s (0.25 m)
2
(0.23 m)
2
0.12 m s
13.63 (a) The period of a vibrating object-spring system is T 2 2
m k , so the spring constant is
k
4
2m
T
2
4
2
2.00 kg
0.600 s
2
219 N m
(b)
If T = 1.05 s for mass m 2 , this mass is
m
kT (219 N/m)(1.05 s)
4 4
2 2
2 2 2
6.12 kg
13.64 (a) The period is the reciprocal of the frequency, or
T
1 1
f 196 s
1
5.10 10
3
s 5.10 ms
(b)
v sound
f
343 m s
196 s
1
1.75 m
13.65 (a) The period of a simple pendulum is T 2
g , so the period of the first system is
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