Freefall chord through the Earth -- calculus proof

[achap01]

so the ODE would be ẍ=a=-gx/R? Im a little confused

 

[haruspex]

so the ODE would be ẍ=a=-gx/R? Im a little confused

Yes, or to put it in its more standard form, $\ddot x+\frac gRx=0$.
Do you recognise that form?

 

[achap01]

Yes, or to put it in its more standard form, $\ddot x+\frac gRx=0$.
Do you recognise that form?

harmonic motion, so angular frequency (rate of oscillation) would be g/R, which have a derivative of 0 with respect to theta?

 

[haruspex]

harmonic motion, so angular frequency (rate of oscillation) would be g/R, which have a derivative of 0 with respect to theta?

Bingo.

 

[kuruman]

Not quite. The angular frequency is $\omega =\sqrt{g/R}.$

 

[achap01]

Bingo.

is there an online or a video proof of this that i can get

 

[kuruman]

What exactly do you want to prove?