Question

Two blocks each of mass m is connected to the spring of spring constant k as shown in the figure.
If the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. The time period of oscillation is

• A. $2\pi \sqrt{\frac{m}{k}}$
• B. $2\pi \sqrt{\frac{m}{2k}}$
• C. $2\pi \sqrt{\frac{m}{4k}}$
• D. $2\pi \sqrt{\frac{2m}{k}}$

Answer 1

Answer: (B)

$2\pi \sqrt{\frac{m}{2k}}$

Reduced mass of the system
$\mu =\frac{\left(m\right)\left(m\right)}{m+m}=\frac{m}{2}$
$\therefore Timeperiod,T=2\pi \sqrt{\frac{\mu }{k}}=2\pi \sqrt{\frac{m}{2k}}$