Chapter 13.1, Problem 41PPSE

Solution

To find: After how many seconds all functions will reach their maximum value.

  $\text{64 s}$

Given:

The two functions having periods of $6\text{ s}$ and $\text{7 s}$ . A new function is added having period of $\text{8 s}$ .

Explanation:

The first two functions having periods $6\text{ s}$ and $\text{7 s}$ will start their beginning together after $6\times 7=42\text{ s}$ .

It may continue further as $42\text{,}84\text{,}\mathrm{126....}$ .

The period of new function starts after $20\text{ s}$ . So,

  $42+20=62\text{ s}$

So, the third function start from $62\text{ s}$ and after each $\text{8 s}$ , it reaches its beginning point. It may continue further as follows $\text{62, 70, 78, 86, 94, 102, 110, 118, 126, }\text{. }\text{. }\text{.}$ .

So, all three functions start their beginning together at $\text{126 s}$ . And this value is $\text{64 s}$ more when the third function reach their maximum.

Conclusion:

Hence, after $\text{64 s}$ seconds all functions will reach their maximum.