Waves and Oscillatiions

[Suvekchhya]

In the equation
v = -A*w*sin(wt + phi )

why must sin(wt+ phi) be = -1 to obtain maximum value of v ?

is there other ways of finding max of v if k = 8n/m, amplitude = 0.1m, and m = 0.5kg?
thankyou

[a.s.h.]

If you consider a graph of v versus t, it varies between +Aω and -Aω, since the coefficient of that sine is -Aω. So v's greatest value is +Aω, which occurs when that sine is equal to -1.

And to find max. v, one can set x = 0 in the equation v² = (k/m).(a² - x²), k is the spring constant, m is the mass and a is the amplitude, and take the positive square root for v.