a 20g mass is suspeneded from the end of a vertical spring having a spring const

Question

a 20g mass is suspeneded from the end of a vertical spring having a spring constatnt of 2880 dynes/cm and is allowed to reach equilibrium. it is then set into motion by stretching the spring 3 cm from its equilibrium position and releasing the mass with an initial velocity of 10 cm/sec in the downward direction. find the position of the mass at any time t if there is no external force and no air resistance. deterimine the circular frequency, the natural frequency and the period for the vibrations.

please show work

Explanation / Answer

From Newton's laws,
0 = -k(yo) - mg (at equilibrium)
yo = -mg/k

my" = -k(y + yo) - mg
y" + (k/m)y = k(yo)/m - g
y" + (k/m)y = 0

Solve the linear differential equation.
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