Determine the average value of the electromotive force `E_(m)` over one period, ie, over the time from t= 0 to t=T, if electromotive force is computed by the formula
`E = E_(0) " sin "(2pi t)/(T)`
where T is the duration of the period in seconds, `E_(0)` the amplitude (the maximum value) of the electromotive force corresponding to the value t= 0.25T. The fraction `(2pi t)/(T)` is called the phase.

Answer

To determine the average value of the electromotive force \( E_m \) over one period, we start with the given formula for electromotive force:

\[ E(t) = E_0 \sin\left(\frac{2\pi t}{T}\right) \]

where \( T \) is the duration of the period in seconds, and \( E_0 \) is the amplitude of the electromotive force.

### Step 1: Set Up the Average Value Formula

The average value of a function \( f(t) \) over the interval from \( a \) to \( b \) is given by:

\[ \text{Average value} = \frac{1}{b-a} \int_a^b f(t) \, dt \]

In our case, we want to find the average value of \( E(t) \) from \( t = 0 \) to \( t = T \):

\[ \text{Average value of } E = \frac{1}{T - 0} \int_0^T E(t) \, dt = \frac{1}{T} \int_0^T E_0 \sin\left(\frac{2\pi t}{T}\right) \, dt \]

### Step 2: Factor Out Constants

Since \( E_0 \) is a constant, we can factor it out of the integral:

\[ \text{Average value of } E = \frac{E_0}{T} \int_0^T \sin\left(\frac{2\pi t}{T}\right) \, dt \]

### Step 3: Evaluate the Integral

To evaluate the integral \( \int_0^T \sin\left(\frac{2\pi t}{T}\right) \, dt \), we can use a substitution. Let:

\[ u = \frac{2\pi t}{T} \quad \Rightarrow \quad du = \frac{2\pi}{T} dt \quad \Rightarrow \quad dt = \frac{T}{2\pi} du \]

Changing the limits of integration:

- When \( t = 0 \), \( u = 0 \)
- When \( t = T \), \( u = 2\pi \)

Now we can rewrite the integral:

\[ \int_0^T \sin\left(\frac{2\pi t}{T}\right) \, dt = \int_0^{2\pi} \sin(u) \cdot \frac{T}{2\pi} \, du = \frac{T}{2\pi} \int_0^{2\pi} \sin(u) \, du \]

### Step 4: Calculate the Integral of Sine

The integral of \( \sin(u) \) over one complete period (from \( 0 \) to \( 2\pi \)) is zero:

\[ \int_0^{2\pi} \sin(u) \, du = 0 \]

### Step 5: Substitute Back

Thus, we have:

\[ \int_0^T \sin\left(\frac{2\pi t}{T}\right) \, dt = \frac{T}{2\pi} \cdot 0 = 0 \]

### Step 6: Final Calculation of Average Value

Substituting back into the average value formula:

\[ \text{Average value of } E = \frac{E_0}{T} \cdot 0 = 0 \]

### Conclusion

The average value of the electromotive force \( E_m \) over one period is:

\[ \boxed{0} \]