Question

A block of mass $m$ is pushed against a spring of spring constant $k$, fixed to one end of the wall. The natural length of the spring is / and it is compressed to half its natural length when the block is released. The velocity of the block as a function of its distance $x$ from the wall is

• A. $\sqrt{\frac{k}{m}(\frac{l^2}{4}-(l-x{)}^2)}$
• B. $\sqrt{\frac{k}{m}(l-x{)}^2}$
• C. $\sqrt{\frac{k}{m}(\frac{l^2}{4}+(l+2x{)}^2)}$
• D. $\sqrt{\frac{k}{m}(l+x{)}^2}$

Answer 1

The correct option is C $\sqrt{\frac{k}{m}(\frac{l^2}{4}+(l+2x{)}^2)}$

$\begin{array}{c}V=w\sqrt{A^2-x^{{}^{\prime }2}}\\ v=\sqrt{\frac{K}{m}}\sqrt{\frac{l^2}{4}-\left(l-x^2\right)}\end{array}$

$A\left(amplitude\right)=$ distance of extra position (v=0) from mean position.

$A=\frac{l}{2}$

$x^{{}^{\prime }}=$displacement of object from mean position so ,

Here,

$x^{{}^{\prime }}=l-x$

Hence,

option $C$ is correct answer.