A load of mass m moves in the xy plane so that its coordinates depend on time according to the law x = Acos wt; y = B sin wt

A load of mass m moves in the xy plane so that its coordinates depend on time according to the law x = Acos wt; y = B sin wt, where A and B are constants. Determine the modulus of the force acting on the load

First, we find the projections of the cargo speed:
Vx = x ‘= (Acos wt)’ = – Awsin wt;
Vy = y ‘= (Bsin wt)’ = Bwcos wt;
Next, we find the projection of the acceleration:
ax = (Vx) ‘= (- Awsin wt)’ = – Aw ^ 2cos wt;
ay = (Vy) ‘= (Bwcos wt)’ = -Bw ^ 2sin wt;

Find the acceleration module:

a ^ 2 = (ax) ^ 2 + (bx) ^ 2 = (- Aw ^ 2cos wt) ^ 2 + (- Bw ^ 2sin wt) ^ 2;

Further, according to Newton’s 2nd law:
F = m * a