The problem states that in the same amount of time, one object oscillates $N_1 = 100$ times, and another object oscillates $N_2 = 400$ times. We need to find the ratio of their periods, $T_1/T_2$.

1. Problem Description

The problem states that in the same amount of time, one object oscillates $N_1 = 100$ times, and another object oscillates $N_2 = 400$ times. We need to find the ratio of their periods, $T_1/T_2$.

2. Solution Steps

Let $t$ be the time interval for which we are given the number of oscillations.

The period $T$ of an oscillation is the time taken for one complete oscillation.

Therefore, the period $T_1$ of the first object is given by $T_1 = t / N_1$.

Similarly, the period $T_2$ of the second object is given by $T_2 = t / N_2$.

We want to find the ratio $T_1 / T_2$.

$T_1 / T_2 = (t / N_1) / (t / N_2) = (t / N_1) * (N_2 / t) = N_2 / N_1$.

Substituting the given values, we get:

$T_1 / T_2 = 400 / 100 = 4$.

3. Final Answer

$T_1/T_2 = 4$