Solution Found!
Consider the pendulum of Figure 7.4, suspended inside a
Chapter 7, Problem 7.11(choose chapter or problem)
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.
Questions & Answers
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.