Sinusoidal Function MCQ Quiz - Objective Question with Answer for Sinusoidal Function - Download Free PDF

Concept:

Fundamental frequency: Fundamental frequency is the minimum frequency of vibration.

nth harmonic of the fundamental frequency is given as:

n^th harmonic = n x fundamental frequency

$f_0=\frac{n^{th}Harmonic}{n}$

Calculation:

Given:

n = 4, 4th harmonic = 512 Hz

∴ The fundamental frequency (f₀) will be:

$f_0=\frac{n^{th}Harmonic}{n}=\frac{512}{4}$

f₀ = 128 Hz

Concept:

Fundamental frequency: Fundamental frequency is the minimum frequency of vibration.

nth harmonic of the fundamental frequency is given as:

n^th harmonic = n x fundamental frequency

$f_0=\frac{n^{th}Harmonic}{n}$

Calculation:

Given:

n = 4, 4th harmonic = 512 Hz

∴ The fundamental frequency (f₀) will be:

$f_0=\frac{n^{th}Harmonic}{n}=\frac{512}{4}$

f₀ = 128 Hz

Concept:

Fundamental frequency: Fundamental frequency is the minimum frequency of vibration.

nth harmonic of the fundamental frequency is given as:

n^th harmonic = n x fundamental frequency

$f_0=\frac{n^{th}Harmonic}{n}$

Calculation:

Given:

n = 4, 4th harmonic = 512 Hz

∴ The fundamental frequency (f₀) will be:

$f_0=\frac{n^{th}Harmonic}{n}=\frac{512}{4}$

f₀ = 128 Hz

The fundamental frequency w₀ = $\frac{201\pi }{2}$

For discrete time sinusoid $\frac{N_0}{m}=\frac{2\pi }{w_0}$

Where m is an integer, and Time period N₀ is also an integer

$\begin{array}{l}{N}_0=\frac{2\pi }{\frac{201\pi }{2}}\times m\\ =\frac{4}{201}\times m\end{array}$

Minimum value of integer m such that N_O is a positive integer is m = 201

$N_0=\frac{4}{201}\times 201$

$\begin{array}{l}y\left(t\right)=6^2{\cos }^2\left(100t+\frac{\pi }{6}\right)\\ \Rightarrow y\left(t\right)=\frac{36\left(1+\cos 2\left(100t+\frac{\pi }{6}\right)\right)}{2}\\ \Rightarrow y\left(t\right)=18+18\cos \left(200t+\frac{\pi }{3}\right)\end{array}$