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Suppose we can change the plane's period of oscillation,

Chapter 13, Problem 104IP

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QUESTION:

Problem 104IP

Suppose we can change the plane's period of oscillation, while keeping its amplitude of motion equal to 30.0 m. (a) If we want to reduce the maximum acceleration of the plane, should we increase or decrease the period? Explain. (b) Find the period that results in a maximum acceleration of 1.0g.

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QUESTION:

Problem 104IP

Suppose we can change the plane's period of oscillation, while keeping its amplitude of motion equal to 30.0 m. (a) If we want to reduce the maximum acceleration of the plane, should we increase or decrease the period? Explain. (b) Find the period that results in a maximum acceleration of 1.0g.

ANSWER:

Solution 104P

Part (a)

Step 1 of 2:

The amplitude of the plane is given and the period is changed during the oscillation. We are going to find the change in maximum acceleration if we change the period.

The expression for the acceleration of oscillatory motion is expressed as

 

Where ⍵ is the angular speed of the motion

        y is the displacement

In the case of maximum amplitude

The relationship between the time period and the angular speed is given by

Therefore

From the above equation, the maximum acceleration is inversely proportional to the time period T and it can be reduced only if we increase the time period T.

Answer: Increase the time period.


Part (b)

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