Answer:
a = 0.563 m/s²
v = 0.225 m/s
Explanation:
The angular frequency is:
ω = 2π / T
ω = 2π / (3.35 s)
ω = 1.88 rad/s
For a spring mass system:
ω = √(k / m)
ω² = k / m
(a) Sum of forces on the mass:
∑F = ma
kx = ma
a = kx / m
a = xω²
When x = 0.160 m:
a = (0.160 m) (1.88 rad/s)²
a = 0.563 m/s²
(b) Energy is conserved. Initial elastic energy = final elastic energy + kinetic energy.
EE₀ = EE + KE
½ kA² = ½ kx² + ½ mv²
½ (k/m)A² = ½ (k/m)x² + ½ v²
½ ω²A² = ½ ω²x² + ½ v²
ω²A² = ω²x² + v²
v² = ω² (A² − x²)
v = ω √(A² − x²)
v = (1.88 rad/s) √((0.200 m)² − (0.160 m)²)
v = 0.225 m/s
