Derivation of angular frequency equation

[AToMic93]

Homework Statement

Derive the angular frequency equation (ω=√(g/L) from following equations:

Homework Equations

1) ((d^2)*θ)/(d*t^2)= (-g/L)*θ
2) θ=θ_maxcos(ωt+δ)

The Attempt at a Solution

I don't even know where to start

 

[gneill]

Homework Statement

Derive the angular frequency equation (ω=√(g/L) from following equations:

Homework Equations

1) ((d^2)*θ)/(d*t^2)= (-g/L)*θ
2) θ=θ_maxcos(ωt+δ)

The Attempt at a Solution

I don't even know where to start

(1) tells you that $\frac{d^2\theta}{dt^2}$ is (-g/L)θ. (2) gives you a formula for θ. If you were only given (2), how would you find an expression for $\frac{d^2\theta}{dt^2}$ from it?

 

[AToMic93]

Would you take the second derivative with respect to time? (giving d²/dt²) then set this equal to the other equation?

 

[gneill]

Would you take the second derivative with respect to time? (giving d²/dt²) then set this equal to the other equation?

I suggest you give it a try

 

[AToMic93]

So the main question I have then is for when I'm deriving how do I deal with the θ_max? Do I treat it just like θ or do I treat it like a constant?

 

[gneill]

So the main question I have then is for when I'm deriving how do I deal with the θ_max? Do I treat it just like θ or do I treat it like a constant?

It is, of course, a constant. But do keep in mind that θ = θ_maxcos(ωt + δ)

 

[AToMic93]

Alright I got it. Thanks