- #1
Karol
- 1,380
- 22
Homework Statement
The restoring force of a pendulum is [itex]F_\theta=-mg\sin\theta[/itex]
and is approximated to [itex]F_\theta=-mg\theta[/itex].
The period is [itex]T=2\pi\sqrt{\frac{L}{g}}[/itex], but can be expressed as the infinite series:
[tex]T=2\pi\sqrt{\frac{L}{g}}\left( 1+\frac{1^2}{2^2}\sin^2\frac{\theta}{2}+\frac{1^2}{2^2}\frac{3^2}{4^2}\sin^4\frac{\theta}{2}+...\right)[/tex]
What is this approximation and of what? i don't think it's a Maclaurin series.
Homework Equations
Maclaurin series of sin(x):
[tex]\sin(x)\cong 1-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}...[/tex]