Question

When a mass m is hung from the lower end of a spring of negligible mass, an extension x is produced in the spring in equilibrium. The mass is set into vertical oscillations. The time period of oscillation is

• A. $T=2\pi \sqrt{\frac{x}{mg}}$
• B. $T=2\pi \sqrt{\frac{gx}{m}}$
• C. $T=2\pi \sqrt{\frac{x}{g}}$
• D. $T=2\pi \sqrt{\frac{x}{2g}}$

Answer 1

The correct option is C

$T=2\pi \sqrt{\frac{x}{g}}$

If k is the force constant, we have $mg=kx$
$\Rightarrow \frac{m}{k}=\frac{x}{g}$
$\therefore T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{\frac{x}{g}}$
Hence, the correct choice is (c).