A spring is stretched 175 mm by an 8-kg block. the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.50 m/s. assume that positive displacement y is downward.

Let spring K be constant

K = F/x = mg/x = (8kg) (9.81 m/s) / 175 * 10⁻³m

= 448.46 N/m

The angular of spring's frequency is

w = √k/√m = √448.46/√8 = 7.49 rad/s

∴ differential equation

y¹¹ + (7.49) ²

y = 0

y¹¹ ₊ 56.1

where y = 0.