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## Homework Statement

The position vector of a particle moving in space is given by

[tex]\vec{r}[/tex]=[tex](1+cos2wt)[/tex][tex]\hat{i}[/tex] [tex]+[/tex] [tex]3sin^{2}wt[/tex][tex]\hat{j}[/tex][tex]+[/tex][tex]3t[/tex][tex]\hat{k}[/tex]

in the ground frame. All the units are in SI. Find the position vector and amplitude of the particle in a frame S moving along the positive z-axis with a velocity 3m/s. Is the line of S.H.M. of the particle parallel to [tex]4/5[/tex][tex]\hat{i}-3/5[/tex][tex]\hat{j}[/tex]?

Attempt:

The P.V. of the frame S at any time t is 3t [tex]\hat{k}[/tex].

From this we can find out the P.V. of the particle w.r.t. the frame S.

I differentiated it w.r.t. time to find out the velocity vector and found Vmax, which is 5w.

Vmax=Aw

so A=5m

Unfortunately, I got both of them incorrect :/