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Physics / Classical Mechanics 0 / Chapter 11 / Problem 11.4

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

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(a) Find the normal frequencies for the system of two

Chapter 11, Problem 11.4

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QUESTION:

(a) Find the normal frequencies for the system of two carts and three springs shown in Figure 11.1, for the case that mi = m2 and k1 = k3, (but k2 may be different). Check that your answer is correct for the case that k1 = k2 as well. (b) Find and describe the motion in each of the two normal modes in turn. Compare with the motion found for the case that k1 = k2 in Section 11.2. Explain any similarities.

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QUESTION:

(a) Find the normal frequencies for the system of two carts and three springs shown in Figure 11.1, for the case that mi = m2 and k1 = k3, (but k2 may be different). Check that your answer is correct for the case that k1 = k2 as well. (b) Find and describe the motion in each of the two normal modes in turn. Compare with the motion found for the case that k1 = k2 in Section 11.2. Explain any similarities.

ANSWER:

Step 1 of 3

The configuration has two elements and

The mass matrix is given by,

..................(1)

The spring constant matrix,

..............(2)

Given the two masses are equal, that is,

Rewriting equation one,

Given so the spring constant matrix will be,

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