Question

Draw signal x(t)=e⁻²|ᵗ|Sin(5t)

Answer 1

In order to draw the signal x(t) = e⁻²|t|sin(5t), analyze the amplitude and frequency of the sine function and plot the graph.

Step-by-step explanation:

To draw the signal x(t) = e⁻²|t|sin(5t), follow these steps:

1. Determine the key properties of the signal:

• - The signal is a combination of exponential decay (e⁽⁻²|ᵗ|⁾) and a sinusoidal wave (sin(5t)).
• - The exponential term affects the amplitude of the sinusoidal wave, causing it to decay as time increases or decreases.
• - The sinusoidal term has a frequency of 5, meaning it completes 5 cycles in one unit of time.

2. Plot the exponential term:

• - Start by plotting the exponential term, e⁽⁻²|ᵗ|⁾, on the y-axis.
• - As |t| increases or decreases, the exponential term decreases exponentially.
• - The exponential term is always positive since e⁽⁻²|ᵗ|⁾is always positive.

3. Plot the sinusoidal term:

• - Now, plot the sinusoidal term, sin(5t), on the y-axis.
• - The sinusoidal wave has a frequency of 5, meaning it completes 5 cycles in one unit of time.
• - The amplitude of the sinusoidal wave is affected by the exponential term, e⁽⁻²|ᵗ|⁾. As |t| increases or decreases, the amplitude decreases.

4. Combine the two plots:

• - Combine the plots of the exponential term and the sinusoidal term on the same coordinate system.
• - The resulting plot represents the signal x(t) = e⁻²|t|sin(5t)

Your question is incomplete, but most probably the full question was:

How to draw signal x(t)=e⁻²|ᵗ|Sin(5t)?