Maximum velocity of a mass undergoing SHM

Question; A 1 g mass is suspended by a spring and executes simple harmonic motion when released. At time t=0 the displacement is 40 cm and acceleration is -3.6 cm/s^2. What is the spring constant k? What is the maximum velocity of this mass? At what time would the modulus of the maximum velocity first be reached?

My attempt:

I done the first part of the question and found k to be 0.025 N/m

Maximum velocity occurs when

v = ωA, and at t=0 x=A?

So hence maximum velocity would be 2 m/s

Using ω^2= k/m

Assuming the above is correct, maximum velocity would first be reached when the

sin(ωt) term is first equal to zero?

Any help would be great 🙂 thanks

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