Does the function y sin 2 wt represents?

Does the function y sin 2 wt represents?

As the acceleration is not proportional to displacement y, the given function does not represent SHM. It represents a periodic motion of angular frequency 2ω.

Is sin 2 a SHM?

The function sin^(2)(omega t) represents: a simple harmonic motion with a pariod π/ω.

How do you find whether a function is SHM or not?

Find the acceleration from the equation representing the displacement and try to relate. The other method is that an SHM usually involves conservation of energy. So try finding total energy. If it is constant, then look for spring like properties, which we usually find in an SHM.

What is the value of sin 2 Omega T?

Hey! If we consider T as time period of that ossilation and w(omega) as the angular velocity of the ossilating particle . Then wT will be equal to 2Π since it has completed one full cycle or complete rotation . And sin(2wT)=sin4Π=0.

Which function represents SHM?

sinωt+cos2ωt.

Does the function y ΩT represent periodic or simple harmonic motion?

As the acceleration is not proportional to displacement hence the function does not represent SHM. It represents a periodic motion of angular frequency 2ω.

Is sin a SHM?

As demonstrated in Mukhopadhyay’s nice answer, sin(ωt)-cos(ωt) is a sinusoid that describes SHM.

Which of the function is harmonic?

harmonic function, mathematical function of two variables having the property that its value at any point is equal to the average of its values along any circle around that point, provided the function is defined within the circle.

What type of function describes simple harmonic motion?

In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM ) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object’s displacement and acts towards the object’s equilibrium position.

Which equation represents SHM?

That is, F = −kx, where F is the force, x is the displacement, and k is a constant. This relation is called Hooke’s law. A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling.

What is not simple harmonic motion?

The motion of a planet around the sun is a periodic motion but not a simple harmonic motion. All other given motions are the examples of simple harmonic motion.

Which of the following functions are periodic but not simple harmonic?

(d) Periodic, but not simple harmonic motion. The given function is cosωt + cos3ωt + cos5ωt. Each individual cosine function represents SHM. However, the superposition of three simple harmonic motions is periodic, but not simple harmonic.

Is y=sin^2(wt) an example of simple harmonic motion?

No, y=sin^2 (wt) is not an example of simple harmonic motion. At first we are to understand that all periodic motions are not simple harmonic motions.

How do you find the differential equation for simple harmonic motion?

Solutions of Differential Equations of SHM. The differential equation for the Simple harmonic motion has the following solutions: x=Asin left ( omega t+phi right) x = Asin(ωt +ϕ) (When the particle at Q at in figure (b) (any time t).

Is it possible to describe simple harmonic motion using coordinates?

Yes. The simple harmonic motion is a to and fro motion about equilibrium position and we can choose our coordinates for describing it. If we designate the displacement from the origin at time t as Which is a differential equation of a SHM with frequency 2ω. This is a a “shifted” oscillator .

What is sin(2wt) =sin4π=0?

If we consider T as time period of that ossilation and w (omega) as the angular velocity of the ossilating particle . Then wT will be equal to 2Π since it has completed one full cycle or complete rotation . And sin (2wT)=sin4Π=0. It also can be understood by drawing a graph of the function , f (t)=sin (wt).