Respuesta :
Answer:
a) Maximum velocity = 0.07 m/s
b) Maximum acceleration = 0.0245 m/s²
c) Position at t = 2s is 0.153 m
d) velocity at t = 2s is - 0.0451 m/s
e) Acceleration at t = 2s is 0.0187 m/s²
Explanation:
x(t) = (0.200 m) cos (0.350t)
The general expression for the displacement of a body in simple harmonic motion = A cos wt
Comparing, A = amplitude = maximum displacement = 0.20 m
w = angular frequency/velocity = 0.350 rad/s
a) v = dx/dt = (d/dt) (A cos wt) = - Aw sin wt
Maximum velocity is given by Aw = 0.2 × 0.35 = 0.07 m/s
b) a = dv/dt = (d/dt) (-Aw sin wt) = - Aw² cos wt
Maximum acceleration = Aw² = 0.2 × 0.35² = 0.0245 m/s²
c) Position at t = 2,
x = A cos wt = 0.2 cos (0.35t)
At t = 2
x = 0.2 cos (0.35 × 2) = 0.2 cos (0.7) = 0.153 m (Take note, wt is in radians)
d) velocity at t=2s
v = - Aw sin wt = - (0.2 × 0.35) sin (0.35 × 2) = - 0.07 sin (0.7) = - 0.0451 m/s
e) Acceleration at t = 2s
a = - Aw² cos wt = - (0.2 × 0.35²) cos (0.35 × 2) = - 0.0245 cos (0.7) = - 0.0187 m/s²
