Some silly question on oscillators

[marmot]

Ok

i know that the solution for the harmonic oscillator differential equation is

x=Acos(wt+d)

However,

I also know that most of the time, atleast in average intermediate mechanics problems the phase difference, d is zero. this baffles me a lot. for example if there is a spring and i stretch it 10 cm and let it go, i know that the phase difference is zero because cosine starts from a maximum and the 10cm i stretched are going to be the maximum. but when does d actually is a value?

 

[marmot]

same question for damped oscillators btw

 

[Meir Achuz]

If there is motion at t=0. For instance if you start it by an impulse.

 

[Bob S]

If you use the representation x = Asin(wt + d), and you release the spring at t = 0, then d = pi/2 radians (90 degrees).