Solution) m = 0.60 kg
K = 30.9 N/m
X = 5 cm = 0.05 m
(a) Maximum speed , Vmax = ?
KE = PE
(1/2)(m)(Vmax)^2 = (1/2)(K)(X)^2
(Vmax)^2 = ((K)(X^2))/(m)
(Vmax)^2 = ((30.9)(0.05^2))/(0.60)
(Vmax)^2 = 0.128
Vmax = (0.128)^(1/2)
Vmax = 0.357 m/s
Vmax = 0.36 m/s
(b) X1 = 1.5 cm = 0.015 m
(1/2)(m)(V^2) = (1/2)(K)(X^2) - (1/2)(K)(X1^2)
V^2 = (K/m)(X^2 - X1^2)
(0.60)(V^2) = (30.9)(0.05^2 - 0.015^2)
(V^2) = (30.9/0.60)(0.00227)
V^2 = 0.1169
V = (0.1169)^(1/2)
V = 0.34 m/s
(c) V = ?
(1/2)(m)(V^2) = (1/2)(K)(X^2) - (1/2)(K)(X1^2)
V^2 = (30.9/0.60)(0.05^2 - 0.015^2)
V^2 = 0.1169
V = (0.1169)^(1/2)
V = 0.34 m/s
(d) x = ?
V = (1/2)(Vmax)
Squaring on both sides
V^2 = (1/4)(Vmax)^2
From above parts
(K/m)(X^2 - X1^2) = (1/4)(K/m)(X^2)
X^2 - X1^2 = (1/4)(X^2)
Here X1 = x
X^2 - (1/4)(X^2) = x^2
(3/4)(X^2) = x^2
x^2 = (3/4)(0.05)
x^2 = 0.0375
x = (0.0375)^(1/2)
x = 0.19 m
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