I require frequency response from transfer function = 1/(s^2+(b/m)*s+k/m) where b= 0.0011, k= 87.88 , m = 0.99 in matlab and i need freq in khz

i require a code for the given graph this is the frequency response from transfer function 1/(s^2+(b/m)*s+k/m) where b= 0.0011, k= 87.88 , m = 0.99

[Sam Chak]

Hi @sia

As you can see from the step response, it is quite oscillatory, and it takes approximately 7,000 seconds to settle down. I am curious to know what specific application you have in mind for this linear second-order system in the real world?

s = tf('s');
b = 0.0011;
k = 87.88; 
m = 0.99;
G = 1/(s^2 + (b/m)*s + k/m)

G =
 
             1
  ------------------------
  s^2 + 0.001111 s + 88.77
 
Continuous-time transfer function.

step(G)

stepinfo(G)

ans = struct with fields:
         RiseTime: 0.1338
    TransientTime: 7.0323e+03
     SettlingTime: 7.0323e+03
      SettlingMin: 1.1174e-05
      SettlingMax: 0.0225
        Overshoot: 99.9659
       Undershoot: 0
             Peak: 0.0225
         PeakTime: 0.3316

Answer 1

[Sam Chak]

Hi @sia

If you simply want to obtain the plot for the "transfer function 1/(s^2 + (0.0011/0.99)*s + 87.88/0.99)," WolframAlpha can generate it for you without the technical details, saving your time and everyone else's. However, to be honest, generating the Bode plot requires fewer characters in MATLAB code compared to WolframAlpha. In other words, MATLAB is faster.

Answer 2

[David Goodmanson]

Hi sia, there is not much need to do any detailed calculation when your starting point is what it is. This system has a small amount of damping so its resonant frequency is very close to

omega =  sqrt(k/m)
   omega = 9.4217
f = omega/(2*pi)
   f = 1.4995

which is what the plot shows. To get a resonant frequency around 1.5 kHz, either k has to increase by 10^6 or m has to decrease by 10^6, or some combination of those has to come up with a factor of 1e6 in the ratio (k/m). [the damping constant b will need a change as well]. So you should go back to the original physical situation. Maybe m is in milligrams instead of kilograms. Lots of possibilities.