Question

system takes 70.40 seconds to complete 20 oscillation. The time period of the system is ( upto correct significant figures)

Answer 1

3.520 s

Answer 2

The time period ($T$) of a system is defined as the time taken for one complete oscillation. It is calculated by dividing the total time taken for a certain number of oscillations by the number of oscillations.

Given: Total time taken for oscillations = 70.40 seconds Number of oscillations = 20

The formula for the time period is: $T = \frac{\text{Total time taken}}{\text{Number of oscillations}}$

Substitute the given values into the formula: $T = \frac{70.40 \text{ s}}{20}$

Now, we perform the division: $T = 3.52 \text{ s}$

Next, we need to determine the correct number of significant figures for the answer. The total time taken is given as 70.40 seconds. The digits 7, 0, 4, and 0 are all significant. The trailing zero after the decimal point is significant. Thus, 70.40 s has four significant figures. The number of oscillations is 20. In the context of counting oscillations, this is an exact integer count. Exact numbers are considered to have infinite significant figures and do not limit the precision of a calculation involving measured values.

When dividing a measured value by an exact number, the result should have the same number of significant figures as the measured value. The measured value (total time) has 4 significant figures. The number of oscillations (exact number) does not limit the significant figures. Therefore, the time period should be expressed with 4 significant figures.

The calculated value is 3.52. To express this value with four significant figures, we add a trailing zero after the decimal point. $T = 3.520 \text{ s}$

Thus, the time period of the system, upto correct significant figures, is 3.520 seconds.