plot sin(1*pi*1000t) +2 where v(t) =1
what does this plot for two periods look liek
funny thing -- it looks like every other sine wave...
http://www.wolframalpha.com/input/?i=sin%281*pi*1000t%29+%2B2
No idea what v(t) has to do with it, though.
To plot the given equation, which is \(v(t) = \sin(1\pi \cdot 1000t) + 2\) for two periods, you need to follow these steps:
1. Determine the period of the function:
The period of a sine function is given by the formula \(T = \frac{2\pi}{\omega}\), where \(\omega\) is the angular frequency. In this case, \(\omega = 1\pi \cdot 1000 = 1000\pi\) since the coefficient in front of \(t\) determines the angular frequency. Therefore, the period is \(T = \frac{2\pi}{1000\pi} = \frac{1}{500}\).
2. Find the time range for two periods:
To plot for two periods, you need to find the time range that covers two complete cycles. Multiply the period by 2: \(2T = 2 \cdot \frac{1}{500} = \frac{2}{500}\).
3. Create a time vector:
Generate a time vector with equally spaced values that cover the desired time range. For example, you can use the linspace function in MATLAB or Python to create a time vector that ranges from 0 to \(\frac{2}{500}\) with a desired number of points. Let's say you want 1000 points, then your time vector could be something like: \(t = \text{linspace}(0, \frac{2}{500}, 1000)\).
4. Calculate the voltage values:
Now, substitute the values of the time vector into the equation \(v(t) = \sin(1\pi \cdot 1000t) + 2\) to obtain the corresponding voltage values. You can calculate this in MATLAB or Python using element-wise multiplication and addition. For example: \(v = \sin(1\pi \cdot 1000t) + 2\).
5. Plot the graph:
Finally, plot the obtained voltage values against the time vector. Use a line plot if you want to connect the points for a continuous waveform. The resulting graph will show two periods of the sine function \(v(t)\) with a constant offset of 2.
Note: Adjust the code and syntax based on the programming language you are using and any specific plotting libraries or functions available.