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# Define Time Response, Natural Response, Force Response

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#### siekiam

##### Newbie level 6
natural response and forced response

Dear all,

Anyone could explain to myself Define Time Response, Natural Response, Force Response.

Hope to hear from you all soon.

Thanks
SieKiam

#### v_c

forced and natural response

Time response of a system is the time evolution of the variables. In circuits, this would be the waveforms of voltage and current versus time.

Natural response is the system's response to initial conditions with all external forces set to zero. In circuits, this would be the response of the circuit with initial conditions (initial currents on inductors and initial voltage on capacitors for example) with all the independent voltages set to zero volts (short circuit) and current sources set to zero amps (open circuit). The natural response of the circuit will be dictated by the time constants of the circuit and in general roots of the characteristics equation (poles).

Forced response is the system's response to an external stimulus with zero initial conditions. In circuits, this would just be the response of the circuit to external voltage and current source forcing function.

Using superposition, the total response of a circuit is the sum of the natural response (response due to initial conditions) and forced response (response due to external forces).

You can also think about this in terms of differential equations. Consider the following first order differential equation for voltage $v(t)$
$\frac{d v(t)}{dt} + v(t) = f(t)$, $v(0)=10V$

The natural response is solving $v(t)$ using the initial condition with $f(t)=0$

The forced resonse is solving for $v(t)$ using $f(t)$ and zero initial condition.

Best regards,
v_c

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sergei_mipt

### sergei_mipt

Points: 2

#### electronics_kumar

forced response natural response

forced response===output for the given input..it is unstable state
naturalresponse===output after input disapears or no input ..ofcourse it is stable state

#### ovii

##### Newbie level 1
natural response: is to check response of inductor and capacitor when no source(both current and voltage) in connected.
forced response : is due the sources(both or only single currnt and voltage ).

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