1D kinematics var Acc (mass on spring)

Question

A mass is hanging from a spring that is moving as v(t) =1.7sin(9.8t)

so the velocity is at 0 m/s on a periodic basis. For example, when t =0s, the velocity is 0m/s. What is the ACCELERATION of the mass when the velocity at the NEXT possible time (after 0 seconds) where the velocity is 0 m/s? Report your answer to the tenths place.

Answer 1

V(t) =1.7 sin(9.8*t) , sin(ωt) = 0 → ωt = kπ for k=1 → ωt = π → t = πT/(2π) → t = T/2

After t=o again velocity will be zero at T/2.

ω = 2π/T → 9.8 = 2π/T → T/2 = π/9.8

a(t) = dV/dt → a(t) = (1.7)(9.8) cos(9.8*t) → a(T/2) = 16.66 cos (9.8*T/2) , a = 16.66 cos(π) = -16.7 m/s²

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When velocity is zero, the mass is in maximum of its amplitude and acceleration is also maximum.