Sinusoidal Definition and 220 Threads

Hi, I having trouble grasping what: "oscillatory motions are sinusoidal in time" means... does this just mean that when solving a problem for simple harmonic motion that the equation is going to involve both and sin/cos and time? Sorry this might be more of a mathematical question.

Can someone please explain the following equation: x = A sin(wt) where A = amplitude, w = angular velocity, t = time. The way it's explained in my textbook is very confusing.

Homework Statement Two sinusoidal waves in a string are defined by the functions y1 = (2.00 cm) sin(20.0x – 32.0t) and y2 = (2.00 cm) sin(25.0x – 40.0t) where y and x are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x...

Hi there. I am having trouble finding an explanation with waves. Suppose that you have to sinusoidal waves y1=Asin(kx-wt) and y2=Asin(kx-wt+phi) If we add them up, the resulting wave will be y=2Acos(phi/2)sin(kx-wt+phi/2). Now, if phi equals pi then the resulting wave will have no...

i posted it in general physics and got not answer. maybe this is the right place for this. thanks here is a question for max dynamic factor for sinusoidal load F*sin(at). say the natural frequency is b for a mass. then the max DLF considering damping is DLF=1/(1-(a/b)^2) when a>>b...

Hi everyone, I'm trying to understand the derivation of D(x,t) = A \sin{(kx - \omega t + \phi_o)} which is the displacement equation for a sinusoidal wave. The way my textbook (Physics for scientists and engineers by Knight) does it: Look at the graph of displacement versus position at time...

The question and attempt to solution is on the attached image. I don't understand why the answer in the textbook is 1.5ym mine is 1.8 ym

I've been working on this one for quite some time... Consider a sinusoidal wave traveling along a string composed of two sections, one with a lighter mass/length density than the other. A pulse is traveling in the light region and about to hit the junction. If the incident wave is given by...

Homework Statement At the time of a full moon, the tides repeat with a period of about 12 hours, and the depth of water in a certain channel varies between 2 meters and 6 meters in a way that can be modeled by an equation of the form D(t) = A + Bsin(ct + d), where A is the average depth and...

Does sinusoidal motion play a special role in physics? Or is it just a mathematical intermediate step or auxiliary? For example of course you can Fourier transform any function, but you might as well chose not to do so and use the normal local differential equation. This way you never...

Homework Statement A sinusoidal sound wave is described by the displacement wave function s(x,t)=(2.00 μm)cos⁡[(15.7 m^(-1) )x-(858 s^(-1) )t] b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 m at t = 3.00 ms Homework...

Homework Statement A satellite is deployed from a space shuttle into an orbit which goes alternately north and south of the equator. Its distance from the equator over time can be approximated by a sine wave. It reaches 4500 km, its farthest point north of the equator, 15 minutes after the...

The book I am currently reading derives the response of an electron to an applied sinusoidal field as: 1/[1 + 2i (w - wa)/g] = 1 / (1 + i delta) where w and wa are the induced and resonance response frequencies and g the damping constant. And delta = 2 (w - wa)/g Up to this...

setting a sinusoidal voltage term, the ODE can be written as (d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt) assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are i(0) = di/dt (0) = 0 i really don't have much of...

What really is a sinusoidal wave current? What exactly is happening to the electrons that is different from a DC? Are there any readings you suggest that will give me more insight into this? Thanks in advance.

In a sinusoidal function...suppose the value of δ is very large...then as x approaches any a, the value of f(x) might not approach L directly...or there should not be a direct relation; example - \lim_{x \to 1.5} sin x = 0.997494986 Where I've stated δ as 7...then if x = 1.5 – 6.9 =...

Homework Statement Prove that f\left(x\right) = \cos(x) + \cos\left(\alpha x \right) where alpha is a rational number, is a periodic function. EDIT: Also, what is it's period? Homework Equations f\left(x\right + p) = f\left(x\right) trig identities The Attempt at a Solution First, I used...

I was routinely checking a question in an Engineering Maths book as listed below: The instantaneous value of voltage in an a.c. circuit at any time t seconds is given by v = 100 sin(50\pit - 0.523) V. Find: (a) the peak-to-peak voltage, the periodic time, the frequency and the phase angle...

Homework Statement The question extends more than this but this is where I have difficulty. An uneven road surface is modeled by a sinusoid with amplitude 25mm and the car is driven at 100km/hr. Use the bode plot calculate earlier to obtain and explain the steady state force response when...

Homework Statement Question: Consider the sinusoidal signal: A*cos(\omegat + \phi) Determine the average power Homework Equations This is my first real attempt in signals and I am really confused with the question... I guess my question would be am I suppose to take the P = lim as t->...

Homework Statement A sound wave is described by D(y,t) = (0.02mm)sin[(8.96 rad/m)y + (3140 rad/s)t + pi/4 rad)], where y is in metres, and t is in seconds. Draw a displacement-versus-time graph D(y=1.00m,t) at y= 1.00 m from t= 0 s and t= 4 ms. Homework Equations D(y,t) = (0.02mm)sin[(8.96...

Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by y(x,t)=(2.5 mm)sin(26.0x -4.0 s-1 * t+0.400 rad), with x in meters and t in seconds. 1.) What is the wavelength of the two waves (m)? [I...

A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

Homework Statement The voltage, V(t), in volts, of a power supply can be modeled by the function V(t) = 110sin5t+15, where t is the time, in seconds. Find the maximum and minimum voltages, within the first second, and the times they occur. Homework Equations The Attempt at a...

Hi Guys, :smile: The following query would sound a bit ridiculous and abstract but it suddenly popped up in my head. :-p What would happen if I were to apply a purely sinusoidal AC voltage across a zero resistance conductor (theoretically, a super conductor) ? Zero resistance would mean...

I'm having a problem with that integration part. The average value of i^2 in one cycle = (sum of all i^2 in that period)/(that period). To derive (sum of all i^2 in that period) we use integration, but that gives the area, how can the area be a substitution for this?...they are different...

I'm trying to work out the displacement of an object, knowing the acceleration, frequency and mass. I've found equations for working it out with the first two, but does the mass have an affect that should be taken into account? This is something very obvious that I will have only been taught...

Problem understanding waves. I can see how rates of speed in circular motion can translate to expressed different kinds/shapes of waves but I don' see why concepts of trigonometry like sin,cos are brought into describing waves. I just feel there could be clearer ways of describing waves.

how does one calculate a gain in signal e.g sine wave. do we take peak-to-peak (or peak) of the output divided by peak-to-peak(or peak) of the input?

Homework Statement Two traveling sinusoidal waves are described by the wave functions y1 = (5.00m) sin[pie(4.00x - 1 200t)] y2 = (5.00m) sin[pie(4.00x - 1 200t -0.250y)] where x, y1, and y2 are in meters and t is in seconds. (a) What s the amplitude of the resultant wave? (b) What is the...

A transverse sinusoidal wave on a string has a period of 25 ms and travels in the negative x direction with a speed of 30 m/s. At t=0, a particle on the string at x=0 has a displacement of 2 cm and is traveling downward with a speed of 2 m/s. Find the amplitude, phase constant, and maximum...

hello!, question about Maxwell equations: a linear restoring force causes simple harmonic motion. In Maxwell equations, what is this restoring force due to? In mechanics to mass and stiffness. do self inductance and capacitance the inertia and the stiffness? HElmholtz eqn resembles the...

Hi, I'm new to the forum so I hope this is the right place to post this, I actually joined to ask this question. I found something in the archive through a google search. The thread can be found at: https://www.physicsforums.com/archive/index.php/t-117265.html Some of the things in there were...

In a paper I am reading it states that since the electric potential (and field) have sinusoidal time dependence, then \Phi(\textbf{x},t)=\Phi(\textbf{x})e^{i\omega t} Why would this equation be true? Why shoudnt the equations read \Phi(\textbf{x},t)=Im(\Phi(\textbf{x})e^{i\omega t})...

Homework Statement Determine the amplitude and phase of the resultant motion when two sinusoidal motions having the same frequency and traveling in the same direction are combined, if their amplitudes are 3.0 cm and 4.0 cm and they differ in phase by pi/2 radians. Homework Equations...

Homework Statement \ddot{\Theta}=C \sin{\Theta} where \Theta is a function of time, and C is a constant. I ran into this on a Lagrangian Equation problem, and though the problem doesn't ask for the solution, I'm wondering how one would solve this Diff EQ. I'm afraid my intro to Diff EQ...

Homework Statement For a sinusoidal wave: At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B? y = (15.0 cm) cos(0.157x - 50.3t) Homework EquationsThe Attempt...

[SOLVED] transverse sinusoidal wave on a string Homework Statement The wavefunction of a transverse sinusoidal wave on a string has the form y(x,t) = A*cos(kx +omega*t + phi), where x and y are in m, t is in s and phi is the phase constant in radians. The wave has a period T = 24.2 ms and...

A sinusoidal wave is traveling on a string with speed 10.00 cm/s. The displacement of the particles of the string at x = 20 cm is found to vary with time according to the equation y = (5.0 cm) sin[16.0 - (8.0 s-1)t]. The linear density of the string is 7.0 g/cm. (a) What is the frequency of the...

hi, is it possible to find the intersect of three different sinusoidal functions without using a graphing calculator? here are the three equations: y=sin (2pi/23)(x) y=sin (pi/14)(x) y=sin (2pi/33)(x) The hint given is that the intersect occurs when y=1

Does the frequency of a sinusoidal voltage or current attribute anything? Maybe more power? All I know so far is that you can filter certain frequencies out with filter circuits.

Homework Statement Consider the sinusoidal wave in the figure, with the wave function below. At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B? y =...

[SOLVED] mechanical waves Homework Statement A sinusoidal transverse wave is traveling along a string in the negative direction of an x-axis. The figure shows a plot of the displacement as a function of position at time t=0; the y-intercept is 4.0m. The string tension is 6.8N, and its linear...

[SOLVED] sinusoidal wave (not sure what to do for the last part)and have test tommoro Homework Statement A sinusoidal wave representing transverse oscillations on a string has the wave function y(x,t)= (0.40m)cos[(10.0\frac{rad} {s})t- 5.00\frac{rad} {m}x] The linear mass density of the...

I have a horrible math teacher this year: she merely shows the steps to solving a problem and doesn't help us understand why and how it works. Homework Statement I need to find the equation for the height of a ferris wheel as it spins. It has a radius of 30m, and a center 18m above ground. It...

Homework Statement Sorry I can't provide a visual for this problem, but I'll try my best to explain it Given: picture of sinusoidal curve with 5 points from left to right, H C D B A H is on downward slope C is a min D is a max B is on upward slope A is on upward slope to the right of B...

Homework Statement What would the geometric explanation of exp(-i*x) be? Homework Equations Exp(-i*x), i being (-1)^1/2 The Attempt at a Solution I'm pretty sure this is just a circle, created clockwise? Just want to check.

Two sinusoidal waves of the same frequency are sent in the same direction along a taut string. One wave has an amplitude of 5.0 mm, the other 8.0 mm. (a) what phase difference between the two waves results in the smallest amplitude of the resultant wave? (b) what is that smallest amplitude? (c)...

pls help me on this problem, thanks a lot. A sinusoidal wave is described by y=(0.30 m)sin(0.20x-40t). Determine the wave speed.

Homework Statement Hi, Could you please help me decide on these answers? The question is " Are the following statements Sinusoidal? And are they Periodic? I have produced the waveforms in MathCad The limits are 0 - 4Pi 1.f(x)= sinx + 2sin(x-(Pi/6)) 2.f(x)= sinx +sin2x 3.f(x)= sinx +...