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3. What is the relationship between "simple harmonic motion" and sinusoidal waves"? Explain as thoroughly as you can:...

Question

3. What is the relationship between "simple harmonic motion" and sinusoidal waves"? Explain as thoroughly as you can:

3. What is the relationship between "simple harmonic motion" and sinusoidal waves"? Explain as thoroughly as you can:



Answers

Explain the period and the frequency of simple harmonic motion. How are they related?

If the object, it's in simple harmonium Muslim, then it's prison is given by disease equal toe A because off omega T or B is equal toe a sign off omega T Now the frequency will be 1/4 Tau omega divided by two by and the senior will be were toe group I divided by Omega. From here, we can say that frequency is equal toe one be ready to buy period where omega is greater than zero

This problem covers the concept of simple harmonic motion and in simple harmonic motion. The force educate, we're into minus of the spring constant K. Into the displacement from equilibrium position And the 4th can bitterness the mass times the acceleration and that it was minus or the spring constant K into the displacement occurs. Or we can write this equation is I'm into D two x upon d. T two equals my nestle here for em X. Right minus of cakes or from this weekend rage Do you two x upon GT two equals minus of key upon em X. Okay, consider key upon them as omega square. So we can't write this. The question is the double differentiation of the position with respect to time equals minus omega squared X. This is a uh differential equation and the solution of the differential equation for X. Candy, he costs omega T. That's fine. Where five is the initial condition and there is the phase angle. Or we can write this is a sign. Omega T plus fire this. So from this you can see the sign and cool cause function described the motion of the particle in simple harmon

Well, in a simple harmonic motion, uh, the the displacement why is given has supposed am patris et on initially seated at extreme positions. So a costa omega T we're gonna get the anger frequency until use any time it which we want to find out why the displacement. So velocity is the No time did the deep obvious this man so divided duty would give me minus a *** a sign or Meg? Artie. So acceleration is the double tracking derivative off publicity. So that is it going to minus on picture or may I square course Omega t. All right, so if you compare e and B here, we can write a as minus a coma guy Square sign 19 plus or minus Omega T. Right. So what we can say is that velocity andi acceleration, huh? Off feed your prints. Oh, 90. This implies when b is Max is Gerald. And where the zero A's Max, let me show you this. So this to you in a graph. So if we consider this in this case, uh, so this is the acceleration. Okay, So is that a time t equal to Gerald? The acceleration is maximum. Then a tactical general velocities. Zero. So, Felicity, with something like this, forget about the amplitude. Okay. Okay. So this is velocity. This is acceleration. So this is how exercise and and the city are collected in a simple harmonic motion to this ends the

Eight. What is meant by oscillation and a simple harmonic motion? So an oscillation is emotion where the displacement of the particle is from the fixed point and it keeps changing direction, so change in direction and it repeats itself. There's some periodicity. Simple harmonic motion is, there is a displacement from equilibrium displacement in the equilibrium, and the acceleration is proportional and opposite of its displacement.


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