Question

When a mass $M$ attached to a spring $X$, as shown in Figure 1, is displaced downwards and released it oscillates with time period $T$.An identical spring is connected in series and the same mass $M$ is attached, as shown in figure 2, then time period will be:

• A. $\sqrt{2}T$
• B. $T$
• C. $2T$
• D. None of the above

Answer 1

The correct option is A $\sqrt{2}T$

In 1st case time period $t=2\pi \sqrt{\frac{m}{k}}$

$k$= spring constant

In second case two string $x$ connected in series.

So, equivalent spring constant

$k^{\prime }=\frac{k\times k}{k+k}=\frac{k}{2}$

So the time period in this case:

$t^{\prime }=2\pi \sqrt{\frac{m}{k^{\prime }}}=2\pi \sqrt{\frac{2m}{k}}$

$t^{\prime }=\sqrt{2}t$