Question

A point moves along the x-axis according to the law x = asin²(ωt — π/4). Find:

(a) the amplitude and period of oscillations; draw the plot x (t);

(b) the velocity projection v_x as a function of the coordinate x; draw the plot v_x (x).

Answer 1

(a) From the motion law of the particle

Now compairing this equation with the general equation of harmonic oscillations:

From eqns(2) and (3),

Plot of v_x(x) is as shown in the answersheet.