Answer:
0.52 m/s
Explanation:
Energy is conserved.
Initial kinetic energy + initial potential energy = final kinetic energy + final potential energy
½ m v₁² + ½ k x₁² = ½ m v₂² + ½ k x₂²
m v₁² + k x₁² = m v₂² + k x₂²
Given:
m = 1.3 kg
k = 52 N/m
v₁ = 0.28 m/s
x₁ = 0.081 m
x₂ = 0.081 m / 2 = 0.0405 m
(1.3) (0.28)² + (52) (0.081)² = (1.3) v² + (52) (0.0405)²
v = 0.52
The velocity halfway to the equilibrium position is 0.52 m/s.
