Question

If two similar springs each of spring constant $K_1$ are joined in series, the new spring constant and time period would be changed by a factor:

• A. $\frac{1}{2},\sqrt{2}$
• B. $\frac{1}{4},\sqrt{2}$
• C. $\frac{1}{4},2\sqrt{2}$
• D. $\frac{1}{2},2\sqrt{2}$

Answer 1

Answer: (A)

$\frac{1}{k_{eq}}=\frac{1}{k_1}+\frac{1}{k_2}$
$\frac{1}{k_{eq}}=\frac{1}{k}+\frac{1}{k}\Rightarrow k_{eq}=\frac{k}{2}$
$k^{\prime }=\frac{k}{2}$
$T=2\pi \sqrt{\frac{M}{k}}$
$T^{\prime }=2\pi \sqrt{\frac{M}{k^{\prime }}}$
$\Rightarrow T^{\prime }=2\pi \sqrt{\frac{M}{k}}\times \sqrt{2}$
$T^{\prime }=\sqrt{2}T$