Question

A mass $M$ attached to a light spring oscillates with a period of $2\text{seconds}.$ If the mass is increased by $2\text{kg},$ the period increases by $1\text{second}.$ What is the value of $M$?

• A. $1.0\text{kg}$
• B. $1.6\text{kg}$
• C. $2.0\text{kg}$
• D. $2.4\text{kg}$

Answer 1

The correct option is B $1.6\text{kg}$

For spring we have $\omega =\sqrt{\frac{k}{m}}$
Thus, $T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{m}{k}}$
Thus, we have
$2=2\pi \sqrt{\frac{M}{k}}$ and $3=2\pi \sqrt{\frac{M+2}{k}}$
or, $M=\frac{k}{{\pi }^2}$ and $M+2=\frac{9k}{4{\pi }^2}$
Solving for $M,$ we have, $M+2=\frac{9M}{4}$ or $M=\frac{8}{5}=1.6\text{kg}$