# very basic maths help

#### harry99932

Joined Dec 30, 2010
38
Hi guys can someone help me out im a verrrrrrry un mathematically minded person slowly learning lol Im trying to expand out this equation but not sure how to go about it.

Vout= Vin* [98+((2/k)*Vin)]

I think im right so far in thinking il end up with;

Vin*98 + Vin*(2/k) + Vin*Vin

Now if thats right, then for the 3rd part of the equation were

Vin= 0.01 sin(2pi800)

i get an equation of the type

(sinx)*(siny)= cos(x-y) - cos(x+y)

How do i apply this to 0.001 sin (2pi800) ? i.e what do i do with the two 0.001's etc?

#### edgetrigger

Joined Dec 19, 2010
133
Hi guys can someone help me out im a verrrrrrry un mathematically minded person slowly learning lol Im trying to expand out this equation but not sure how to go about it.

Vout= Vin* [98+((2/k)*Vin)]

I think im right so far in thinking il end up with;

Vin*98 + Vin*(2/k) + Vin*Vin

just this => Vin*98 + Vin*(2/k) * Vin

#### edgetrigger

Joined Dec 19, 2010
133
Vin= 0.01 sin(2pi800)

i get an equation of the type

(sinx)*(siny)= cos(x-y) - cos(x+y)

How do i apply this to 0.001 sin (2pi800) ? i.e what do i do with the two 0.001's etc?

correct formula is

sinx * siny = 1/2 * [cos(x-y) - cos(x+y)]

#### edgetrigger

Joined Dec 19, 2010
133
i could not get what you want to do with Vin.

If Vin is a sine wave the equation would be Vin = Vmax* Sin(θ+phy)

[ i did not get the symbol for phy in ]

could you pls let me know what you want to do with Vin

#### harry99932

Joined Dec 30, 2010
38
Hi edgetrigger,

The 0.01 sin(2*pi*800) is definatley correct. Peak sine wave voltage is 0.01 at 800hz working from equation; Vpeak sine (ωτ) were t is irrelevant for now and 2*pi*800 is hertz to angular velocity

the equation is the input to output expression for a theoretical amplifier, were v out = the equation given below, the answer should be several (3 we think) voltages a dc component, fundamental frequency and a harmonic frequency.

The previous example we are given is

Vo= 0.001 + 9.962Vi + 0.1Vi^2 with Vin at 0.01 sin (2000*pi*t) we get a result of

0.001005 + 0.09962sin(2000*pi*t) - 5x10^-6cos(4000*pi*t)

0.001005 volts dc
0.09962 volts ac at 1000hz fundamental frequency
5x10^-6 volts ac at 2000hz second harmonic

Any ideas??

#### Georacer

Joined Nov 25, 2009
5,182
The answer is delayed, but, hey, I deserve some christmass free time.

Let me try this one:

$$V_{out}=V_{in}(98+\frac2kV_{in})\\ =98V_{in}+\frac2kV_{in}V_{in}\\ =9.8\sin (1600\pi t) +\frac2k 0.0001 \sin^2 (1600 \pi t)\\ 9.8 \sin(1600 \pi t) + \frac2k 0.0001 \left( \frac12 (1- \cos (3200 \pi t)) \right )\\ =\frac{0.0001}{k}+9.8 \sin (1600 \pi t)- \frac{0.0002}{k} \cos (3200 \pi t)$$

So, I guess your assumptions where correct.

I used the formula proposed by edgetrigger.

As usual, any corrections are welcome.