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I'm supposed to derive x as a function of time for a simple

harmonic oscillator (ie, a spring). According to my textbook

this is done by using newton's second law and hooke's law

as this: ma=-kx and one gets a differential equation in

the second order. I can follow the calculations until this

happens: (see attached picture)

(where omega is the frequency)

I do get the equation (1) when I solve the differential

equation myself but I don't understand how equation (1) translates

to (2)????

I assume this must be done by using some trigonometric law?

if so then which one and how??

Thanks

harmonic oscillator (ie, a spring). According to my textbook

this is done by using newton's second law and hooke's law

as this: ma=-kx and one gets a differential equation in

the second order. I can follow the calculations until this

happens: (see attached picture)

(where omega is the frequency)

I do get the equation (1) when I solve the differential

equation myself but I don't understand how equation (1) translates

to (2)????

I assume this must be done by using some trigonometric law?

if so then which one and how??

Thanks