What is Sinusoidal: Definition and 229 Discussions
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in both pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:
where:
A, amplitude, the peak deviation of the function from zero.
f, ordinary frequency, the number of oscillations (cycles) that occur each second of time.
ω = 2πf, angular frequency, the rate of change of the function argument in units of radians per second
φ
{\displaystyle \varphi }
, phase, specifies (in radians) where in its cycle the oscillation is at t = 0. When
φ
{\displaystyle \varphi }
is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.
The sine wave is important in physics because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.
##\require{physics}##The given circuit is this:
The question is taken from this video. The Professor has solved it using Phasor analysis, the final solution being $$\begin{equation}
i_x(t) = 7.59 \sin \qty( 4t + 108.4^\circ )~\mathrm{amps}.
\end{equation}$$My aim, however, is to use Laplace...
For part(a) of this problem,
The solution is,
I don't understand why they assume on the graph where that the waveform is during it's phase. For example, could it not also be correctly drawn as shown in red:
Could it not?
Many thanks!
For part(a) of this problem,
The solution is,
However, why did they not have a point at (x,y) = (0, -3) initially? Also why did they not do a y against time graph?Many thanks!
Hello all, I have a random sequences question and I am mostly struggling with the last part (e) with deriving the marginal pdf. Any help would be greatly appreciated.
My attempt for the other parts a - d is also below, and it would nice if I can get the answers checked to ensure I'm...
Greetings,
is it possible to characterize a sinusoidal wave in the domain of time and then pass into the domain of movement along x direction?
I start with: a is the amplitude of the sine function and ω is the angular velocity. t is the time. I can express the angular velocity in funct. of the...
Hi PF!
I have a vector valued function ##f(s) = r(s)\hat r + z(s)\hat z## that plots a line in the ##r##,##z## plane when I use ParametricPlot. I'd like to plot this line into a surface, so that it revolves around the ##z## axis, but in a sinusoidal fashion. Basically I'd like to revolve it...
The transition probability -- the probability that a particle which started out in the state ##\psi_a## will be found, at time ##t##, in the state ##\psi_b## -- is
$$P_{a \to b} = \frac{|V_{ab}|}{\hbar^2} \frac{sin^2[(\omega_0 - \omega)t/2]}{(\omega_0 - \omega^2}.$$
(Griffiths, Introduction...
The owner of an ice cream shop kept records of the average number of sales per month for 2019. Create a sinusoidal equation to model this information of number of sales per month.I found the maximum, minimum for this, but how can I find the period of from this table.
As I already know formula to...
Sinusoidal Functions... Can someone help me with this.
Describe the transformations that are applied to y= -4cos[2(x-30°)] +5 (State any shifts, stretches, compressions, or reflections).
What property of a sinusoid makes it so special? I understand Fourier analysis, but really you could do Fourier using any periodic function as the building block.
Sinusoids really do seem to be fundamental though, if you narrow the pass band of a filter with any random signal you will get a...
Fitness function for window length of filter
On a sinusoidal signal with amplitude 1, and period P, an exponential moving average (EMA) (with alpha = 1/n), and a linear weighted moving average (LWMA) (with window length n) are calculated; when you subtract the EMA from the LWMA, it can be seen...
I had previously solved this using Root Mean Square method by integrating the value of voltage from t=0 to t=T/2 and then from t=T/2 to t=T.Answer was Vo/2½.Yesterday I found this question👇🏾
if I followed the previous approach then:
5 volts is not even in the option. How can I find the DC...
I(k_x, k_y) = \int_{0}^{R} \int_{0}^{2\pi} J_{m-1}(\alpha \rho) \sin((m + 1) \phi) e^{j\rho(k_x \cos\phi + k_y \sin\phi)} \rho d\rho d\phi Is there any way to do it? J is the Bessel function of the first kind. I thought of partially doing only the phi integral as \int_{0}^{2\pi} \sin((m + 1)...
Hi,
Please have a look on the attachment. The displacement of swing from the equilibrium position, x=0, is considered to be maximum, +x, when the swing reaches the person who is pushing it. The pushing force is of short duration and could be approximated by a pulse. I hope I have it correct...
Hi,
Most of the spring vibration lectures assume spring to be fixed on one end and mass on the other end [Example]. In my case, spring has a sinusoidal excitation on one end and mass on other end. Pl. refer the image below.
How to get the governing equation? With that I also want to find the...
My simplistic derivation below for a Class A amplifier shows that an AC signal at the input produces DC, fundamental, and 2nd harmonic terms at the output. This seems to contradict most the information I have found on this - which just states that the output is sinusoidal and of the same...
Homework Statement
What is the derivative of ##f(x)=\frac {2x^2} {cos x}##?
Homework EquationsThe Attempt at a Solution
##F(x)=\frac {2x^2} {cos x}##
So...
##f(x)=2x^2## and ##f'(x)=4x##
##g(x)=cosx## and ##g'(x)=-sinx##
If I plug these into the quotient rule I thought that I would get...
hello everyone, i have a problem related with sinusoidal steady-state analysis, the problem is like this :
the circuit for the question is like this :
i am still unable to find the answer for the question (b), the answer i got is not the same as the one provided by the question above, my...
Hello,
For a project I am working on, I am trying to design a 2D with parallel sinusoidal patterns. Imagine a 2D section of a pipe (two parallel surfaces with distance in between). Each surface is basically a sine function. Peak points meet with each other, as well as troughs. Liquid is...
Homework Statement
Graph ##y=tan\left(x-\frac {π}{4}\right)##
Homework Equations
N/A
The Attempt at a Solution
To graph a tangent function, I first find the vertical asymptotes to set the boundaries for the graph:
To do so, set what's inside the parentheses equal to ##\frac π 2## and ##-\frac...
Homework Statement
Express the following in the form x = Re{Aeiαeiωt}
(a) x= cos(ωt) + sin(wt)
(b) x= sin(ωt +π/4) + cos(ωt)
(c) x= 2cos(ωt+π/3) + (√3)sin(ωt)-cos(ωt)
Homework Equations
cos x = 1/2 e^ix + 1/2 e^-ix
sin x = − i/ 2e^ix + i/2 e^−ix
The Attempt at a Solution
To be honest, I have...
Homework Statement
This isn't really part of my homework, my homework was to draw a pretty graph, but I am curious about some behavior.
I was given a picture of a sinusoidal function. I found it was ##2sin(\frac{\pi}{3}t-\frac{\pi}{6}) + 6##. Then I used trig identities to get...
$\tiny{7.t.27}$
$\textsf{Write an equation for a sinusoidal graph with the following properties:}\\$
$$A=-3,
\textsf{Period}=\frac{2\pi}{3},
\textsf{Phase Shift}=-\frac{\pi}{4}$$
\begin{align*}\displaystyle
A&=-3\\
T&=\frac{2\pi}{3}=\frac{2\pi}{\omega}\\
\omega&=3\\...
Sinusoidal wave form ?
I am asking:
We know that if a coil rotates in a transverse magnetic field a sinusoidal voltage is induced between its terminals.
.
My question now is:
Why it is exactly sinusoidal in the shape and not any other wave shape??
.
Homework Statement
Two sinusoidal waves in a string are defined by the wave functions
y1 = 2.00 sin (20.0x – 32.0t)
y2 = 2.00 sin (25.0x – 40.0t)
where x, y1, and y2 are in centimeters and t is in seconds.
(a) What is the phase differencebetween these two waves at the point x = 5.00 cm at t...
Hello, guys.
In field oriented control of ac machines, the electromagnetic torque is proportional to the q-axis current. We can control instantaneous torque by control the q-axis current. If the torque we want is a constant value,with PI controller, no problem, no steady error. But if we want to...
Homework Statement
R = 1 kohm and Vs(t) is sinusoidal of (peak) amplitude 3 V. The diode is modeled by the series combination of an ideal diode and 0.7 V voltage source.
For what percentage of time will the diode conduct?
answer: 42.5
Homework EquationsThe Attempt at a Solution
I'm...
Homework Statement
Evaluate the Fourier Transform of the damped sinusoidal wave g(t)=e^{-t}sin(2\pi f_ct)u(t) where u(t) is the unit step function.
Homework Equations
\omega =2\pi f
G(f)=\int ^{\infty}_{-\infty} g(t)e^{-j2\pi ft}dt
sin(\omega _ct)=\frac{e^{j\omega _ct}-e^{-j\omega _ct}}{2j}...
Hi everyone,
Thank you in advance for taking the time to read my question and for your help. I really appreciate it.
The question is set out as follows:
Given the set
𝑆 = {𝑎 sin (𝑥+𝑏) | 𝑎, 𝑏 E R}.
The addition of elements 𝒔1, 𝒔2 ∈ 𝑆 is defined as follows:
𝒔1 +𝒔2 =𝑎1 sin (𝑥+𝑏1)+𝑎2 sin...
Homework Statement
Homework Equations
none
The Attempt at a Solution
-amplitude is 3
-period is 180°
-right 60°
-down 1
Rough sketch of graph:
I would like to know if the graph looks right, is there any improvements to be made?
Thanks :)
Homework Statement
Homework Equations
3. The Attempt at a Solution a) The height of the high tide is 4.5 m
b) The height of the low tide is 0.25 m
c)
Period = 12.5 hours k= 360/12.5 = 28.8
amplitude = 2.125 m
vertical shift = 2.375 m
phase shift = it doesn't look like there is any...
Hello,
How do you solve Schroedinger's equation (time-independent, in one dimension) if the potential is V=sin(x)? Do you have to use the series approximation for sin(x) and obtain a series solution for psi? Is there some way to use Bloch's theorem since the potential is periodic? I've only...
Homework Statement
Homework Equations
The Attempt at a Solution
a) Here is a sketch of the graph. The lowest point on the Ferries Wheel is 2.5 m and the highest point is 2.5 m + 50.5 m = 53 m. It completes a full cycle every 120 seconds and starts at the lowest point.
b) The highest...
Homework Statement
A sinusoidal wave is propagating along a stretched string that lies along the x-axis. The displacement of the string as a function of time is graphed in the figure (attachment) for particles at x=0m and x=0.0900m.
(A) What is the amplitude of the wave?
4mm
(B) What is the...
Homework Statement
(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A = 5.00 cm, λ =85.0 cm, f = 5.00 Hz, and y(0, t) = 0 at t = 0. (Use the following as necessary: x...
Homework Statement
In sinusoidal circuit shown in Figure 13 is known : w =10^6 1/s, R = 100 Ohm ,
L = 300μH , C1 = 10nF and C2= 5nF . Reactive power of coil inductance L is QL = 3kVAr ,
RMS value of the voltage receiver impedance Z is UZ = 100 V , and the voltage UZ phase delaying behind...
I'm reading Griffiths' section on the infinite square well defined as having zero potential between 0 and a on the x-axis and being infinite everywhere else, and am confused about the following part when discussing the general solution inside the well. The bolded part is what confuses me, the...
My textbook states the following:
The wave disturbance travels from x=0 to some point x to the right of the origin in an amount of time given by x/v, where v is the wave speed. So the motion of point x at time t is the same as the motion x=0 at the earlier time t-(x/v). Hence we find the...
Homework Statement
Hi! I'm trying to find the points of intersection of a sinusoidal function and a line. The line is y=x/7. The function is y=sinx. Can someone tell me how to determine the number of intersections and exact intersections. I would also like to know if the same method can be...
Suppose we have two laser diodes that are made to transmit light at the same wavelength and intensity. Also, suppose that we place them in an open space and separate them by a distance such that when their generated beams intersect at one point in space and one point only. Further suppose that...
Homework Statement
"Suppose that a hydrogen atom, initially in its ground state, is placed in an oscillating electric field ##\mathcal{E}_0 \cos(\omega t) \mathbf{\hat{z}}##, with ##\hbar \omega \gg -13.6\text{eV}##. Calculate the rate of transitions to the continuum."
Homework Equations
##R =...