How Does the Transfer Function Affect Sinusoidal Inputs?

[noobish]

Homework Statement

This is related to the frequency response topic.
Given transfer function G(s) = 4/(s+1)
and input is sinusoidal i.e. 2 sin (10t + 10)

Homework Equations

None.

The Attempt at a Solution

I have found out that the magnitude of the transfer function G(s) is 4/sqrt(101) with phase angle -84 degree.

Is the output
(4/sqrt(101) + 2) sin (10t - 74) ?
because that is what i was told.

All these while I thought that the magnitude of G(s) have to be multiplied with the magnitude of the input sinusoidal to obtain the magnitude of the output. But in this case, he just add both of them together.
Please clarify. =)

 

[CEL]

Homework Statement

This is related to the frequency response topic.
Given transfer function G(s) = 4/(s+1)
and input is sinusoidal i.e. 2 sin (10t + 10)

Homework Equations

None.

The Attempt at a Solution

I have found out that the magnitude of the transfer function G(s) is 4/sqrt(101) with phase angle -84 degree.

Is the output
(4/sqrt(101) + 2) sin (10t - 74) ?
because that is what i was told.

All these while I thought that the magnitude of G(s) have to be multiplied with the magnitude of the input sinusoidal to obtain the magnitude of the output. But in this case, he just add both of them together.
Please clarify. =)

First of all the 10 in sin(10t + 10) is radians, so you can not add it to -84 degree and obtain 74 radians.
And yes, the gain of the transfer function must be multiplied by and not summed to the amplitude.