Is the Velocity Equation for SHM Correctly Derived Without Calculus?

[ProPM]

Hi

I am a bit lost with the equations for velocity:

I don't know Calculus yet, so my teacher just gave me the equation:

-wx₀cos(wt) (w being omega)

He then said: v₀ = wx₀

and therefore, concluded: -v₀cos(wt)

and then for when the displacement is maximum at time = 0: v₀cos(wt)

Is this correct? I mean, I am obviously not doubting him but I am a bit confused plus my notes were not very organized on this day...

Thanks in advance

 

[rl.bhat]

when t =0, ωt = 0 and cos(ωt) = 1

So vo = -xo*ω

 

[ProPM]

So the equation would be:

v₀cos(wt)

and for sin, how would it work?

 

[mukundpa]

The sign and the function sin or cos depends on the instant you are taking t=0. If t is taken zero when the particle is at the equilibrium position (x=0) than the equation for displacement will be x= A sin wt and that for velocity will be v = Aw cos wt

thus at extreme position wt = 90 deg, gives x = A and v = 0.
(A is amplitude and Aw = Vo, the maximum velocity)