If the velocity v(t)=-2sint+3cost, when does mass pass through the equilibrium position for the fist time?

Question

An elastic band is hung on a hook & a mass is hung on the lowere end of the band. When the mass is pulled downward and then released, it vibrates verticaly. The equation of this motion is s(t)=2cos(t)+3sin(t),t> or = 0

Answer 1

You call equilibrium position s(t) =0 or v(t) =0 ???
in the first case
2cos t +3 sin t = 0 tan t = -2/3 and t=2.554
in the second case
-2 sin t+3 cos t=0 and tang t = 3/2 so t=0.983+pi =4.124

Answer 2

Mass Pass

Answer 3

equilibrium position is when Force = 0.
since F = M (dV/dt), you need to find when does dV/dt = 0.
dV/dt = -2cost - 3sint = 0
solve for "t" in the above eqn and get the ans
hint : t = tan inverse (-2/3)