1
a). Y(t) = Yo*cos(ωt) ,

Yo = 18cm
ω = 2π/T = 2π/0.6s = 10.47rad/s

Y(t) = 0.18cos(10.47t)

b) Y(t) = 0m

0.18cos(10.47t) = 0
cos(10.47t) = 0

10.47t = π/2
t = 0.15s

c). V(t) = Y'(t) = - ωYosen(ωt)

V(t) = - 10.47*0.18sin(10.47t)

V(t) = - 1.8846sin(10.833t) ,

como el sen de algo puede tener como maximo valor 1

Vmax = ± 1.8846m/s

d). a(t) = V'(t) = - ω²Yocos(ωt)

a(t) = - (10.47)²*0.18cos(10.47t)

a(t) = - 19.73cos(10.47t)

2

x = Asen(2πft)
A = 0.38
f = 6.50/(2π) ≈ 1.0345 Hz
T = 1/1.0345 = 0.966
v = 2.47 cos(6.50t)
E = 1/2 * mv^2 = (1/2)300(2.47)^2 = 915.135 J


a 9 cm o 0.09m

0.09 = 0.38 sin 6.50t
sin 6.50t1 = 0.09/0.38 = 0.23684
cos 6.50t1 = (1 - 0.23684^2)^(1/2) = 0.97155

v1 = 2.47(0.97155) = 2.3997

Ec1 = (1/2)(300)(2.3997)^2 = 863.80125 J
Ep1 = 915.135 - 863.80125 = 51.33375 J