Ballistic Pendulum speed of a bullet

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Homework Statement


The speed of a rifle bullet may be measured by means of
a ballistic pendulum in the following way. The bullet, of
known mass m and unknown speed v, embeds itself in a
stationary wooden block of mass M, suspended as a pen-
dulum of length L. This sets the block to swinging. The
amplitude x of swing may be measured and, using conser-
vation of energy, the velocity of the block immediately after
impact may be found. Assume that x(double less than sign)L. Show that the
speed of the bullet is given by

Vb=[(m+M)/m]X(g/L)^(1/2)


Homework Equations


K=(1/2)mV^2
U=mgh
P=mV
Vw=velocity of wooden block

The Attempt at a Solution


Ok here's what I did I got part of the problem I went all the way to
Vb=[(M+m)/m](2gh)^(1/2)
The problem is going from (2gh)^(1/2) to X(g/L)^(1/2)
I used angular frequency and it seems to work but I'm not sure plus we haven't talked about that in class. Another way it seems to work is from radial acceleration but only if the radius = X which i think might be possible but not always. Watching a video from an MIT lecture I saw that it can be done using cosine expansion but I don't know how to.

Any help will be highly appreciate, thanks in advance.
 

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