The displacement vector of a particle of mass m is given by r (t) = `hati A cos omega t + hatj B sin omega t`.
(a) Show that the trajectory is an ellipse.
(b) Show that F = `-m omega^(2)r`.

Explanation

To solve the problem step by step, we will break it into two parts as requested.

### Part (a): Show that the trajectory is an ellipse.

1. **Given Displacement Vector**:
The displacement vector of the particle is given by:
\[
\mathbf{r}(t) = A \cos(\omega t) \hat{i} + B \sin(\omega t) \hat{j}
...