Creating a Signal Vector with Given Conditions

I'm required to create the following signal in MATLAB with sampling rate of 1000 samples per second and with 200 samples.

X = sin(50*pi*t) + 2*sin(100*pi*t)

I have done this as follows

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   Fs = 1000; %Sampling Rate
   N = 200; %Number of Samples 
   n = 0:N-1 %Numbering the Samples

   x = sin(50*pi*Fs*n/N) + 2*sin(100*pi*Fs*n/N);
   plot (x)

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               and

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   Fs = 1000; %Sampling Rate
   N = 200; %Number of Samples 
   t = 0:N/Fs:N-1 %Sampling Time 

   x = sin(50*pi*t) + 2*sin(100*pi*t);
   plot (x)

-------------------------------------------------------------------

However, both these plots are different from each other. Can someone explain why they are different please ?

Answer 1

[Image Analyst]

Hint: Look at what your time variable is in each of the cases, and especially if the delta t between adjacent time elements makes sense given the sampling rate. Try to put the first term into the standard form sin(2*pi*omega*t) and see what omega (the frequency) is. Also note that sampling rate is independent of the frequency (or period).

You might want to use linspace() instead.