Question 183: Oscillations

Question

As per given figures, two springs of spring constants $$k$$ and $$2 k$$ are connected to mass $$m$$. If the period of oscillation in figure (a) is $$3 \mathrm{s}$$, then the period of oscillation in figure (b) will be $$\sqrt{x}~ s$$. The value of $$x$$ is ___________.

Accepted Answer

For case (a),
$${K_{eq}} = {{2K} \over 3}$$
For case (b),
$${K_{eq}} = 3K$$
$$\because$$ $$T = 2\pi \sqrt {{m \over K}} $$
$$	herefore$$ $${{{T_a}} \over {{T_b}}} = \sqrt {{{{K_b}} \over {{K_a}}}} $$
$${3 \over {{T_b}}} = \sqrt {{{3K 	imes 3} \over {2K}}}  = {3 \over {\sqrt 2 }}$$
$${T_b} = \sqrt 2 $$
$$x = 2$$

Oscillations

As per given figures, two springs of spring constants $k and 2 k are connected to mass m. If the period of oscillation in figure (a) is 3 \mathrm{s}, then the period of oscillation in figure (b) will be \sqrt{x}~ s. The value of x$ is ___________.

Integer / Numeric Answer Type