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zimovet [89]
3 years ago
7

Find the power and the rms value of the following signal square: x(t) = 10 sin(10t) sin(15t)

Engineering
1 answer:
ArbitrLikvidat [17]3 years ago
8 0

Answer:

\mathbf{P_x =25 \ watts}

\mathbf{x_{rmx} = 5 \ unit}

Explanation:

Given that:

x(t) = 10 sin(10t) . sin (15t)

the objective is to find the power and the rms value of the following signal square.

Recall that:

sin (A + B) + sin(A - B) = 2 sin A.cos B

x(t) = 10 sin(15t) . cos (10t)

x(t) = 5(2 sin (15t). cos (10t))

x(t) = 5 × ( sin (15t + 10t) +  sin (15t-10t)

x(t) = 5sin(25 t) + 5 sin (5t)

From the knowledge of sinusoidial signal  Asin (ωt), Power can be expressed as:

P= \dfrac{A^2}{2}

For the number of sinosoidial signals;

Power can be expressed as:

P = \dfrac{A_1^2}{2}+ \dfrac{A_2^2}{2}+ \dfrac{A_3^2}{2}+ ...

As such,

For x(t), Power  P_x = \dfrac{5^2}{2}+ \dfrac{5^2}{2}

P_x = \dfrac{25}{2}+ \dfrac{25}{2}

P_x = \dfrac{50}{2}

\mathbf{P_x =25 \ watts}

For the number of sinosoidial signals;

RMS = \sqrt{(\dfrac{A_1}{\sqrt{2}})^2+(\dfrac{A_2}{\sqrt{2}})^2+(\dfrac{A_3}{\sqrt{2}})^2+...

For x(t), the RMS value is as follows:

x_{rmx} =\sqrt{(\dfrac{5}{\sqrt{2}} )^2 +(\dfrac{5}{\sqrt{2}} )^2 }

x_{rmx }=\sqrt{(\dfrac{25}{2} ) +(\dfrac{25}{2} ) }

x_{rmx }=\sqrt{(\dfrac{50}{2} )}

x_{rmx} =\sqrt{25}

\mathbf{x_{rmx} = 5 \ unit}

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lara [203]

Answer:

0.845\ \text{N}

Explanation:

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Change in acceleration due to gravity due to change in altitude is given by

g_h=g(1+\dfrac{h}{R})^{-2}\\\Rightarrow g_h=9.81\times(1+\dfrac{4205}{6371000})^{-2}\\\Rightarrow g_h=9.797\ \text{m/s}^2

Weight at sea level

W=mg\\\Rightarrow W=65\times 9.81\\\Rightarrow W=637.65\ \text{N}

Weight at the given height

W_h=mg_h\\\Rightarrow W_h=65\times 9.797\\\Rightarrow W_h=636.805\ \text{N}

Change in weight W_h-W=636.805-637.65=-0.845\ \text{N}

Her weight reduces by 0.845\ \text{N}.

8 0
3 years ago
The density of a certain type of steel is 8.1 g/cm3. What is the mass of a 100 cm3 chunk of this steel
irina1246 [14]

Answer:

  810 g

Explanation:

Mass is the product of density and volume:

  m = ρV

  m = (8.1 g/cm³)(100 cm³) = 810 g

The mass of the chunk is 810 grams.

4 0
2 years ago
The volume of microbial culture is observed to increase according to the formula
saw5 [17]

The expression of V(m³)=e^(t(s)) to make V in in³ and t in minutes is;

V(in³) = (¹/₆₁₀₂₄)ae^{\frac{1}{60}bt(h)

We are given that;

Volume of microbial culture is observed to increase according to the formula;

V = e^(t)

where;

t is in seconds

V is in m³

We want to now express V in in³ and t in minutes.

Now, from conversions;

1 m³ = 61024 in³

Also; 1 second = 1/60 minutes

according to formula for exponential decay, we know that;

V = ae^(bt)

Thus, we have;

61024V = ae^(¹/₆₀b(t(h))

V(in³) = (¹/₆₁₀₂₄)ae^{\frac{1}{60}bt(h)

Read more about subject of formula at; brainly.com/question/790938

3 0
2 years ago
Solar energy stored in large bodies of water, called solar ponds, is being used to generate electricity. If such a solar power p
fgiga [73]

Answer: 1.137*10^7 Btu/h.

Explanation:

Given data:

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3 0
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According to the decreasing order of toughness. list the following materials (note: the steels are assumed to have no cold work
fiasKO [112]

Answer:

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Explanation:

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Modulus of toughness can be defines as the area of stress-strain diagram up to fracture point.Modulus of toughness is the property of material.

So the decreasing order of toughness can be given as follows

1090 Steel >1040 Steel > Pure aluminium >Diamond.

8 0
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