Hello!
Denote the starting force as the mass as
the stiffness of a spring as
and the finish time as
The starting time is
Also denote the displacement of a mass as
let a spring moves to the left and its final position is
Then we know from Newton's Second law that Also we know Hooke's law,
(minus sign because
acts to the left but...
Hello!
Denote the starting force as the mass as
the stiffness of a spring as
and the finish time as
The starting time is
Also denote the displacement of a mass as
let a spring moves to the left and its final position is
Then we know from Newton's Second law that Also we know Hooke's law,
(minus sign because
acts to the left but
compresses a spring to the right).
So we obtain a differential equation for
And we know and
(a mass starts from rest) and
The general solution is
From the bounding conditions we have and
Because we obtain
the first time it is when
or
Our goal is to find
This is the final formula. The magnitude of the velocity in numbers is 4.24 (m/s).
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