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Q. 17

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 415

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Short Answer

The position of a oscillating mass is given by , where is in . Determine:

a. The amplitude.

b. The period.

c. The spring constant.

d. The phase constant.

e. The initial conditions.

f. The maximum speed.

g. The total energy.

h. The velocity at .

See the step by step solution

Step by Step Solution

Step 1: Definition of Oscillating mass:

The simplest mechanical oscillating system is a mass coupled to a linear spring that is subject to gravity. When the weight of the mass is balanced by the tension of the spring, the system is in equilibrium.

Step 2: Given values are:

Required for:

Step 3: Part (a) - The given equation for amplitude is:

Step 4: Part (b) - The given time T is:

Step 5: Part (c) - The given spring constant is:

Substitute in (1),

Step 6: Part (d) - The given phase constant is:

Step 7: Part (e) - The given initial constant is:

Step 8: Part (f) - The given velocity is: 

The absolute velocity is the maximum speed:

Step 9: Part (g) - The system's maximum energy storage capacity is:

Step 10: Part: (h) -  In order to acquire velocity replacement in (2):

Step 11: The final result is:

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