The problem asks to find the value of $k$ in the equation $15\sin(kt)$ such that the period of the function is $\frac{6}{5}$ seconds.

1. Problem Description

The problem asks to find the value of $k$ in the equation $15\sin(kt)$ such that the period of the function is $\frac{6}{5}$ seconds.

2. Solution Steps

The general form of a sinusoidal function is $A\sin(Bx)$, where $A$ is the amplitude and the period is given by the formula:

$Period = \frac{2\pi}{|B|}$

In our case, the function is $15\sin(kt)$. Thus, $B = k$. The period is given as $\frac{6}{5}$. We can set up the equation:

$\frac{6}{5} = \frac{2\pi}{|k|}$

We solve for $|k|$:

$|k| = \frac{2\pi}{\frac{6}{5}} = 2\pi \cdot \frac{5}{6} = \frac{10\pi}{6} = \frac{5\pi}{3}$

Since we are not given any further information, we can assume $k$ to be positive.

$k = \frac{5\pi}{3}$

3. Final Answer

The value of $k$ should be $\frac{5\pi}{3}$.