Answer:
y (t) = 0.754 * cos ( 7.96 t - 69.52)
Explanation:
Given:
m = 1.5 kg , k = 95 N / m , v₀ = 6 m / s , d = 0.35 m , t = 0
y (t) = A * cos ( ω * t - φ )
Using the equation that describe the motion
m * v = - k * x ⇒ m * x'' = - k * x
Angular velocity is equal to
ω = √ k / m ⇒ ω = √ 95 N /m / 1.5 kg
ω = 7.96 rad /s
A = v / ω ⇒ A = 6 m /s / 7.96 rad / s
A = 0.754
d = cos * φ ⇒ φ = cos ⁻¹ * 0.35
φ = 69.52
y (t) = A * cos ( ω * t - φ ) ⇒ y (t) = 0.754 * cos ( 7.96 t - 69.52)