Pre-class Quiz

Enter your student number Read Taylor 6.1, 6.2, 7.1

Question 1 The integral \(\int_{x_1}^{x_2}x\sqrt{1-y'^2}dx\) (where \(y'=\frac{dy}{dx}\)) is stationary on a path \(y=y(x)\) represented by one of the following:
a) Circle
b) \(arcsinh\) function
c) Cycloid

Select one:

a)
b)
c)

Question 2 Mass m moves on an incline of angle \(\alpha\). Coordinates are: x is horizontal and y is along the plane. The Lagrangian is given by:

1)\(\space \mathscr{L}=\frac{m(\dot{x}^2+\dot{y}^2)}{2}-mgcos\alpha\)

2)\(\space \mathscr{L}=2m(\dot{x}^2+\dot{y}^2)+mgsin\alpha\)

3)\(\space \mathscr{L}=\frac{m(\dot{x}^2+\dot{y}^2)}{2}+mgysin\alpha\)

4)\(\space \mathscr{L}=(\dot{x}^2+\dot{y}^2)-gy\)

Choose one option:

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Lecture 18
- Pre-class Quiz
  - l_18_4

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