- #1

Vitani11

- 275

- 3

## Homework Statement

An equation of motion for a pendulum:

(-g/L)sinΦ = Φ(double dot)

## Homework Equations

L = length

g = gravity

ω = angular velocity

Φ

_{ο}= initial Φ

## The Attempt at a Solution

The solution is Φ=Asinωt+Bcosωt

solving for A and B by setting Φ and Φ(dot) equal to zero respectively gives:

Φ= Φ

_{ο}cosωt

My question is how can you just go ahead and write down Φ=Asinωt+Bcosωt? My professor said it was because this was the only function that when differentiated twice give -sinωt but I can't just take that for what it is because I need to know how to arrive there.