 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2018

Paper 4

The equation of motion is
$$
m\ddot x=-V'(x).
$$
Multiplication by $\dot x$ gives
$$
\frac d{dt}\left(\frac12m\dot x^2+V(x)\right)=\dot x(m\ddot x+V'(x))=0,
$$
so the <mechanical energy> $E=\frac12m\dot x^2+V(x)$ is conserved. On a segment where the direction of motion is fixed,
$$
\boxed{t-t_0=\pm\sqrt{\frac m2}\int_{x_0}^{x}\frac{du}{\sqrt{E-V(u)}}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 4 / 3A / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 4 / 3A / d / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 4 / 3A / d / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)