Question

question 20
a 0.25 kg mass attached to a spring oscillates with a period of 1.0 s. what would its period be if the mass were increased to 1.0 kg?
○ 4.0 s
○ 0.50 s
○ 0.25 s
○ 2.0 s
○ 1.0 s

Explanation:

Step1: Recall spring period formula

The period of a mass-spring system is $T = 2\pi\sqrt{\frac{m}{k}}$, where $m$ is mass and $k$ is spring constant.

Step2: Relate two periods

For the same spring, $k$ is constant. So $\frac{T_2}{T_1} = \sqrt{\frac{m_2}{m_1}}$.

Step3: Substitute values

$m_1 = 0.25\ \text{kg}$, $T_1 = 1.0\ \text{s}$, $m_2 = 1.0\ \text{kg}$.
$\frac{T_2}{1.0} = \sqrt{\frac{1.0}{0.25}} = \sqrt{4} = 2$.
Thus $T_2 = 2.0\ \text{s}$.

Answer:

D. 2.0 s