Page 118 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

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13. The equivalent spring constant of two parallel springs with stiffnesses k 1 and k 2 is
1 1 1
(a) k 1 + k 2 (b) (c) +
1 1 k 1 k 2
+
k 1 k 2
14. The equivalent spring constant of two series springs with stiffnesses k 1 and k 2 is
1 1 1
(a) k 1 + k 2 (b) (c) +
1 1 k 1 k 2
+
k 1 k 2
15. The spring constant of a cantilever beam with an end mass m is
3EI l 3 Wl 3
(a) (b) (c)
l 3 3EI 3EI
16. If f1-t2 = f1t2, function f(t) is said to be
(a) even (b) odd (c) continuous

1.5 Match the following:

1. Pythagoras (582–507 b.c.) a. published a book on the theory of sound
2. Euclid (300 b.c.) b. first person to investigate musical sounds on a
scientific basis
3. Zhang Heng (132 a.d.) c. wrote a treatise called Introduction to Harmonics
4. Galileo (1564–1642) d. founder of modern experimental science
5. Rayleigh (1877) e. invented the world’s first seismograph
1.6 Match the following:

1. Imbalance in diesel engines a. can cause failure of turbines and aircraft engines
2. Vibration in machine tools b. cause discomfort in human activity during metal
cutting
3. Blade and disk vibration c. can cause wheels of locomotives to rise off the track
4. Wind-induced vibration d. can cause failure of bridges
5. Transmission of vibration e. can give rise to chatter

1.7 Consider four springs with the spring constants:
k 1 = 3500 N>m, k 2 = 8500 N>m, k 3 = 17,500 N>m, k 4 = 35,000 N>m

Match the equivalent spring constants:
1. k 1 , k 2 , k 3 , and k 4 are in parallel a. 16,007.75 N/m
2. k 1 , k 2 , k 3 , and k 4 are in series b. 52,500 N/m
3. k 1 and k 2 are in parallel 1k eq = k 12 2 c. 64,500 N/m
4. k 3 and k 4 are in parallel 1k eq = k 34 2 d. 3310.078 N/m
5. k 1 , k 2 , and k 3 are in parallel 1k eq = k 123 2 e. 2044.674 N/m
6. k 123 is in series with k 4 f. 61,000 N/m
7. k 2 , k 3 , and k 4 are in parallel 1k eq = k 234 2 g. 29,500 N/m
8. k 1 and k 234 are in series h. 12,000 N/m