solution:
the spring force exerted by spring with spring constant k is given by
[tex]F(x)=-kx[/tex]
where k is spring constant
and x is deformation of spring
in order to calculate word done by the spring
[tex]W=\int\limits^L_0 {} \, dW[/tex]
the work done by the spring as it is compressed from x=0 to x=L
[tex]W=-kx^2/2[/tex]
inserting the limits x=0 and x=L
we get work done in terms of k and L
[tex]ANSWER[/tex]
[tex]W=-kL^2/2[/tex]
The work done by the spring when it is compressed , is [tex]-\frac{kL^{2} }{2}[/tex]
The Restoring fore in spring is given as,
[tex]F=-kx[/tex]
Where k is spring constant.
Since , spring is moved from x= 0 to x = L
[tex]workdone=\int\limits {F} \, dx[/tex]
[tex]W=\int\limits^0_L-k {x} \, dx \\\\W=-\frac{kx^{2} }{2}[/tex]
Substituting the limit of integration.
[tex]W=-\frac{kL^{2} }{2}[/tex]
Therefore, The work done by the spring when it is compressed , is [tex]-\frac{kL^{2} }{2}[/tex]
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