Question

A spring is stretched by $5\text{cm}$ by a force $10\text{N}$. The time period of the oscillations when a mass of $2\text{kg}$ is suspended by it is

• A. $3.14\text{s}$
• B. $0.628\text{s}$
• C. $0.0628\text{s}$
• D. $0.314\text{s}$

Answer 1

The correct option is B $0.628\text{s}$

For a spring, $kx=F$

Given, $x=5\text{cm},F=10\text{N}$

$\Rightarrow k(5\times {10}^{-2})=10$

$\Rightarrow k=\frac{1000}{5}=200\text{N/m}$

Now, for spring-mass system undergoing SHM,

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

given, $m=2kg$

$\Rightarrow T=2\pi \sqrt{\frac{2}{200}}=\frac{2\pi }{10}=0.628\text{s}$

Hence, $\left(A\right)$ is the correct answer.