Question

A force of $6.4N$ stretches a vertical spring by $0.1m$. The mass that must be suspended from the spring so that it oscillates with a period of $\left(\pi /4\right)$seconds is

• A. $\left(\frac{\pi }{4}\right)kg$
• B. $1kg$
• C. $\left(\frac{1}{\pi }\right)kg$
• D. $10kg$

Answer 1

Answer: (B)

$1kg$

$6.4=kx$
$6.4=k\times 0.1$
$k=64$
$T=2\pi \sqrt{\frac{m}{k}}$
$\frac{\pi }{4}=2\pi \sqrt{\frac{m}{k}}$

$\frac{1}{64}=\frac{m}{64}$

$m=1kg$