Chapter 16

(a) $1\text{.}\text{23}\times {\text{10}}^3\text{N/m}$

(b) $6\text{.}\text{88 kg}$

(c) $4\text{.00 mm}$

(a) 889 N/m

(b) 133 N

(a) $6\text{.}\text{53}\times {\text{10}}^3\text{N/m}$

(b) Yes

16.7 ms

$\mathrm{0.400\; s}/\text{beats}$

400 Hz

12,500 Hz

1.50 kHz

(a) 93.8 m/s

(b) $\text{11}\text{.}3\times {\text{10}}^3\text{rev/min}$

$2\text{.}\text{37}\text{N/m}$

0.389 kg

94.7 kg

1.94 s

6.21 cm

2.01 s

2.23 Hz

(a) 2.99541 s

(b) Since the period is related to the square root of the acceleration of gravity, when the acceleration changes by 1% the period changes by $(0\text{.}\text{01}{)}^2=0\text{.}\text{01\%}$ so it is necessary to have at least 4 digits after the decimal to see the changes.

(a) Period increases by a factor of 1.41 ($\sqrt{2}$)

(b) Period decreases to 97.5% of old period

Slow by a factor of 2.45

length must increase by 0.0116%.

(a) $\text{1.99 Hz}$

(b) 50.2 cm

(c) 1.40 Hz, 71.0 cm

(a) $3\text{.}\text{95}\times {\text{10}}^6\text{N/m}$

(b) $7\text{.}\text{90}\times {\text{10}}^6\text{J}$

a). 0.266 m/s

b). 3.00 J

$\pm \frac{\sqrt{3}}{2}$

384 J

(a). 0.123 m

(b). −0.600 J

(c). 0.300 J. The rest of the energy may go into heat caused by friction and other damping forces.

(a) $5\text{.}\text{00}\times {\text{10}}^5\text{J}$

(b) $\text{1.20}\text{×}{\text{10}}^3$ s

$f=\text{4 Hz}$

462 Hz,

4 Hz

(a) 3.33 m/s

(b) 1.25 Hz

0.225 W

7.07

16.0 d

2.50 kW

$\text{3.38}\times {\text{10}}^{\text{–5}}{\text{W/m}}^2$