Hello, can anybody help me ? one question about simple harmonic oscillation

[wowolala]

1. Homework Statement [/b]

Let Z(t)=(3/4)Sin(2π/3t) be the equation for a SHO in the Z diection about z=0.

1. what are the amplitude, phase, frequency, angular frequency and period of this SHO?

2. what is the maximum velocity? what is the maximum acceleration?

3. when Z= 3/4, what are the velocity and acceleration?

4. when z=0, what are the velocity and acceleration?

Could someone solve all question for me, i am so confused in this part .

thx so much

 

[Shooting Star]

You must show some attempt, however bad you think it is. Write the meanings of the various symbols in SHM, and then try to see what is given here. You WILL get help.

 

[ogb p]

Hello,

I can definitely help you with your questions about simple harmonic oscillation. Let's start by defining some terms. Simple harmonic oscillation (SHO) is a type of motion where an object oscillates back and forth between two points due to a restoring force that is proportional to the displacement from equilibrium. In your case, the object is moving in the Z direction about z=0, and the equation for this motion is Z(t)=(3/4)Sin(2π/3t).

Now, let's answer your questions one by one:

1. The amplitude of an SHO is the maximum displacement from equilibrium, which in this case is 3/4. The phase is the initial position of the object when the motion begins, and in this case, it is 0 since the object starts at equilibrium. The frequency is the number of complete oscillations per unit time, which is 2π/3 in this case. The angular frequency is the frequency multiplied by 2π, so it is 4π/3. The period is the time it takes for one complete oscillation, which is 3 seconds in this case.

2. The maximum velocity occurs when the object passes through equilibrium, and it is equal to the angular frequency multiplied by the amplitude, so it is 3m/s. The maximum acceleration occurs at the points of maximum displacement from equilibrium, and it is equal to the angular frequency squared multiplied by the amplitude, so it is 9m/s^2.

3. When Z=3/4, the velocity is 0 since the object is at equilibrium. The acceleration is equal to the angular frequency squared multiplied by the displacement from equilibrium, so it is 9/16m/s^2.

4. When Z=0, the velocity is equal to the maximum velocity, which is 3m/s. The acceleration is equal to the maximum acceleration, which is 9m/s^2.

I hope this helps clarify your confusion. Let me know if you have any other questions. Happy to help!