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Consider the pendulum of Figure 7.4, suspended inside a

Chapter 7, Problem 7.11

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QUESTION:

Consider the pendulum of Figure 7.4, suspended inside a railroad car, but suppose that the car is oscillating back and forth, so that the point of suspension has position \(x_{\mathrm{s}}=A \cos \omega t, y_{\mathrm{s}}=0\). Use the angle \(\phi\) as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of \(\phi\) and vice versa.

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QUESTION:

Consider the pendulum of Figure 7.4, suspended inside a railroad car, but suppose that the car is oscillating back and forth, so that the point of suspension has position \(x_{\mathrm{s}}=A \cos \omega t, y_{\mathrm{s}}=0\). Use the angle \(\phi\) as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of \(\phi\) and vice versa.

ANSWER:

Step 1 of 3

The suspension of bob

                                                       

                                                         

Here  is the amplitude,  is the angular velocity and is the time.

From the figure the component of the pendulum

                                                            

Here,  is the length of pendulum and  is the angle.

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