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The block's oscillation frequency is 1.1 Hz.
The block's distance from equilibrium when the speed is 57 cm/s is 14.2 cm.
The block's distance from equilibrium at t = 7.0 s is 10.37 cm.
The oscillation frequency of the block is calculated as follows;
f = 1/2π√(k/m)
f = 1/2π √(9/0.19)
f = 1.1 Hz
ω = 2πf
ω = 2π x 1.1
ω = 6.91 rad/s
x(t) = A cos(ωt + Φ)
ωX sin(Ф) = v
6.91 x 29 sin(Ф) = 116
sin(Ф) = 116/200.39
sin(Ф) = 0.579
Ф = arc sin(0.579)
Ф = 0.62 rad
29 = A cos(6.91 x 0 + 0.62)
29 = A cos(0.62)
29 = A(0.814)
A = 35.63 cm
when the speed is 57 cm/s, the distance of the block is calculated as follows;
ωX sin(Ф) = v
(6.91)X sin(0.62) = 57
X(4.015) = 57
X = 57/4.015
X = 14.2 cm
x(t) = A cos(ωt + Φ)
x(7) = 35.63 cos(6.91 x 7 + 0.62)
x(7) = 10.37 cm
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