# How to define system from a given equation

1. Mar 19, 2014

### aguntuk

1. The problem statement, all variables and given/known data
Input-output description of a system y(t) = S{v(t)} with S{v(t)} = sin[ωct+k.v(t)]

Wanted:
(a) Meaning of this system?
(b) Is this system
(i) linear?
(ii) time-invariant?

2. Relevant equations

3. The attempt at a solution

(b)

(i) For a system to be linear, the superposition principle can be applied to the above equation, i.e., additivity property & homogeneity (scaling) property will have to be satisfied.

as far my calculation, the system is non-linear. Am i correct?

(ii) For a system to be time-invariant, time-shifting property should be satisfied. In this can, the system is time-variant, i.e., non time-invariant. Am i correct?

Please let me know your thoughts. specially (a) Meaning of this system. Also let me know whether I am correct or not for (b) (i) & (ii)

2. Mar 19, 2014

### Staff: Mentor

You need to define all of the terms before you can answer the questions. In particular, is c a constant? and what is meant by k.v(t)?

3. Mar 19, 2014

### aguntuk

Dear berkeman,
here is the question in the attachment.

#### Attached Files:

• ###### Ques_System.jpg
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4. Mar 19, 2014

### Staff: Mentor

Ah, that's different!

$$y(t) = sin[ω_ct + kv(t)]$$

(click the Quote button to see how I used LaTeX to enter the equation -- there is a tutorial on LaTeX in the Feedback forum)

Start by graphing the function with y(t) on the vertical axis and t on the horizontal axis. What does the function look like?

5. Mar 19, 2014

### Staff: Mentor

Also, is there any hint in the problem (or the text leading up to the problem) what v(t) is supposed to represent? Or are you just supposed to guess what it is?

6. Mar 20, 2014

### aguntuk

No other hints except the text, i think v(t) is arbitrary.....i am lost here how to represent it? Am i correct for 2nd part of linearity & time invariance?

7. Mar 20, 2014

### Staff: Mentor

Could v(t) be velocity in the y direction? That is,

$$v_y(t) = \frac{dy(t)}{dt}$$

It's hard to believe that v(t) is arbitrary. Can you clarify the question with your instructor or TA?

8. Mar 20, 2014

### aguntuk

The thing is it is a test for an exam not in a course & i can't ask the authority also!!!!

9. Mar 20, 2014

### Staff: Mentor

What do you mean that it is for an exam? Is it from a take-home exam for one of your courses?