# How to define system from a given equation

• aguntuk
In summary: If so, can you provide more information, such as the name of the course and the name of the test?What do you mean that it is for an exam? Is it from a take-home exam for one of your courses?If so, can you provide more information, such as the name of the course and the name of the test?
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?

## 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)

aguntuk said:

## 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?

## 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)

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)?

Dear berkeman,
here is the question in the attachment.

#### Attachments

• Ques_System.jpg
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aguntuk said:
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?

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?

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?

aguntuk said:
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?

berkeman said:
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!

aguntuk said:
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?

## 1. What is a system in the context of an equation?

A system in the context of an equation refers to a set of elements or variables that are interconnected and interact with each other to produce a desired outcome or result.

## 2. How do you identify a system from a given equation?

To identify a system from a given equation, look for a set of variables or components that are related and affect each other's values. These variables will be connected through mathematical operations such as addition, subtraction, multiplication, or division.

## 3. What are the different types of systems that can be defined from an equation?

There are two main types of systems that can be defined from an equation: linear systems and non-linear systems. Linear systems have a constant rate of change, while non-linear systems have a varying rate of change.

## 4. How do you solve a system of equations to define the system?

To solve a system of equations, you can use various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to find the values of the variables that satisfy all equations simultaneously, thus defining the system.

## 5. Can a system be defined by only one equation?

No, a system cannot be defined by only one equation. A system requires multiple equations to define the relationships between variables and accurately describe the behavior of the system.

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