Physics - SHM Question with Solution | TestHub

Elongation in spring is given by$x=\frac{m}{k}\left(g_{eff}\right)$

When the cage is moving up by acceleration$a$

$x_1=\frac{m}{k}(g+a)$

When the cage is moving down with acceleration$a$

$x_2=\frac{m}{k}\left(g-a\right)$

When the cage is moving with acceleration$a$horizontally

$x_3=\frac{m}{k}\sqrt{g^2+a^2}$

$\left[\mathrm{m}=\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{ }\mathrm{k}=\mathrm{s}\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}\right]$

$using {\left(1\right)}^2+{\left(2\right)}^2$

$\therefore x_1^2+x_2^2=\frac{m^2}{k^2}.2(g^2+a^2)=2x_3^2$

$\Rightarrow \mathrm{ }{x}_3=\sqrt{\frac{x_1^2+x_2^2}{2}}$