Question

A mass m is attached to two strings as shown in figure. The spring constants of two springs are K_1 and K_2. For the frictionless surface, the time period of oscillation of mass m is

• A. $2 \pi \sqrt{\frac{m}{K_1-K_2}}$
• B. $\frac{1}{2 \pi} \sqrt{\frac{K_1-K_2}{m}}$
• C. $\frac{1}{2 \pi} \sqrt{\frac{K_1+K_2}{m}}$
• D. $2 \pi \sqrt{\frac{m}{K_1+K_2}}$

Answer 1

Answer: (D)

$2 \pi \sqrt{\frac{m}{K_1+K_2}}$

Answer 2

Both the springs are in parallel.
$\begin{aligned} & K_{e q}=K_1+K_2 \\\ & T=2 \pi \sqrt{\frac{m}{K_{e q}}}=2 \pi \sqrt{\frac{m}{K_1+K_2}} \end{aligned}$