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A spring mass system is characterized by the equation of motion:

m a = F = m d² x / d t² = - k x d² x/ d t² = - k/m x = - ω₀² x

the solution for displacement at time t is given by : x = A Cos (ω₀ t + Ф)

ω₀ is the natural frequency of the system for simple harmonic motion. = √(k/m) = √(16/1) = 4 rad /sec. angular frequency is 4 rad /sec.

A = amplitude of the vibration = 0.20 metes. Ф = initial phase of the system, given by

Cos Ф = x₀ / A , where x₀ = the position of mass from the mean position when the oscillation has started.

displacement x = A Cos (ω₀ t + Ф) differentiate : dx/dt = v = velocity of mass m at time t v = - A * ω₀ sin (ω₀ t + Ф) v = - 0.20 * 4 Sin (ω₀ t + Ф)

v = dx/dt = - 0.80 Sin 4 t if the initial phase = 0°.