Question

The motion of a particle is given by x = A sin3(ωt).

(a) Enter an expression for the amplitude of the particle's motion.
(b) Enter an expression for the particle's velocity, v.
(c) Enter an expression for the particle's acceleration, a.
you cannot use v in the answers, and all trig functions can only contain (ωt).

Answer 1

The amplitude of the particle's motion is A. The velocity of the particle is v = 3Aω cos^2(ωt). The acceleration of the particle is a = -9Aω^2 sin(ωt) cos(ωt).

Step-by-step explanation:

(a) The formula x = A sin^3(ωt) represents simple harmonic motion, where A represents the amplitude of the particle's motion. In this case, A is the amplitude of the displacement.

(b) The velocity of the particle can be found by taking the derivative of the displacement equation with respect to time. Thus, v = 3Aω cos^2(ωt).

(c) The acceleration of the particle can be found by taking the derivative of the velocity equation with respect to time. Therefore, a = -9Aω^2 sin(ωt) cos(ωt).