Question

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?

Answer 1

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