How to define system from a given equation

[aguntuk]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

(a) I don't know how to define this system & what is the question is asking to be answered, please help me out.

(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)

 

[berkeman]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

(a) I don't know how to define this system & what is the question is asking to be answered, please help me out.

(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)

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)?

 

[aguntuk]

Dear berkeman,
here is the question in the attachment.

 

[berkeman]

Dear berkeman,
here is the question in the attachment.

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?

 

[berkeman]

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?

 

[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?

 

[berkeman]

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?

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?

 

[aguntuk]

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?

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

 

[berkeman]

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

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