The x component of the velocity of an object vibrating along the x-axis obeys the equation vx(t) = (0.445 m/s) sin[(25.4 rad/s)t + 0.223].
(a) What is the amplitude of the motion of this object?
(b) What is the maximum acceleration of the vibrating object?
vx(t) = v0 sin(wt + p)
where
v0 = A w
A = amplitude [m]
w = pulsation [rad/s]
p = phase [rad]
then
a)
A = v0 /w0.0175
A = 0.445/25.4 = 0.0175 m = 1.75 cm
b)
a = dv/dt
ax(t) = v0 w cos(wt + p)
maximum acceleration is
ax(t) = v0 w = A w^2
ax(t) = 0,0175 * 25.4^2 = 11,3 m/s^2
The x component of the velocity of an object vibrating along the x-axis obeys the equation...
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