# Archived 'Kinematics - Vector Derivative' Exercise

#### portuguese

1. Homework Statement
I'm studying for a Mechanics exam and I have a doubt on a 'Kinematics - Vector Derivative' exercise. I don't know how to begin and that's my main problem.

Well, this is the exercise:

Some data:

This mechanical system comprises:

- Body 1: A T-shaped arm, with mass 'm', that rotates around the vertical axis Z0 with constant angular velocity 'theta point'.

- Body 2: A cursor with mass 'm2' which moves along the arm OC, being linked to O by a spring of stiffness 'K'

- Body 3: A arm with mass 'm3', articulated in C with Body 2, and that rotates around the axis Y2 with angular velocity 'fi point' and angular aceleration 'fi 2 points'.

Find out:

a) The absolute velocity and aceleration of the point C using the vector derivatives expressed in S2.
b) The absolute velocity and aceleration of the point G3 using the vector derivatives expressed in S2.
c) The absolute velocity and aceleration of the point C using the vector derivatives expressed in S3.
d) The absolute velocity and aceleration of the point G3 using the vector derivatives expressed in S3.

Can someone explain me how to start?

Thanks a lot!

2. Homework Equations

3. The Attempt at a Solution
I just need an idea to know how to start... :\
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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#### akshay86

is the movement of cursor is a part of the system.(it suffers a psudo force in x-dir=Zo/2*theeta2 )
so it's movement away from the Zo axis is easier

#### akshay86

the rotation of body3 also influence the centrifugal force on the cursor and distance it moved against spring force
when body3' z3 axis become parallel to z2 axis total mass=m2+m3 cursor moves x distance from equilibrium position where kx=(m2+m3)(a+x)(theeta point)^2
when body3 moves 90degrree and z3 become parallal to x1 axis,C behind G3 cursor moves x1 distance where kx1=(m2+m3)(a+x1+m3b/(m2+m3))(teeta point)^2
where m3b/(m2+m3) is positn of c.m
when G3 behind C on x axis ie,cursor move 270degree cursor moves x2 distance where kx2=(m2+m3)(a+x2-m3b/(m2+m3))(theeta point)^2
ie, here cursor is oscillating according to the rotation of body3.so we have to connect these 2 motions and apply their equation of motion together to answer this question
this is only a opinion if not better ignore

"'Kinematics - Vector Derivative' Exercise"

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