Simple Harmonic Motion: Maximum Velocity and Acceleration Calculation

In summary, the equations for determining the maximum velocity and acceleration of a body oscillating with simple harmonic motion are v = ωAcos(ωt) and a = -ω^2Asin(ωt). Additionally, the maximum velocity occurs when cos(ωt) is at its maximum, which corresponds to the maximum value of the graph y = sinx. The relationship between ω and the frequency is ω = 2πf. Therefore, the maximum velocity can also be calculated as vmax = ωA.
  • #1
daveiejbeer
6
0
The total movement of a body oscillating with simple harmonic motion is 200mm. If the frequency of oscillation is 6Hz, determine the maximum velocity and maximum acceleration of the body.

I missed the class when this was done so I haven't got the notes. I am not sure if this is right but I found these equations

v = w Acos wt
a = -w2 Asin wt = -w2y

Anyone point me in the right direction please?
 
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  • #2
daveiejbeer said:
The total movement of a body oscillating with simple harmonic motion is 200mm. If the frequency of oscillation is 6Hz, determine the maximum velocity and maximum acceleration of the body.

I missed the class when this was done so I haven't got the notes. I am not sure if this is right but I found these equations

v = w Acos wt
a = -w2 Asin wt = -w2y

Anyone point me in the right direction please?

If you know v=ωA*cosωt

vmax will occur when cosωt is maximum, so cosωt is what number?
 
  • #3
I found this info http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm so I am reading this.
 
Last edited by a moderator:
  • #4
Im still none the wiser!
 
  • #5
daveiejbeer said:
I found this info http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm so I am reading this.

daveiejbeer said:
Im still none the wiser!

Well let's start simple. For the graph of y=sinx, what is the maximum value of y? (the graph oscillated between?)


what is the relationship between ω and the frequency?
 
Last edited by a moderator:
  • #6
Is the max value of y 1? Going back to trig and waveforms.
Isn't ω 2∏ times the frequency?
 
  • #7
daveiejbeer said:
Is the max value of y 1? Going back to trig and waveforms.
Isn't ω 2∏ times the frequency?

Right, so wouldn't

vmax=ωA ?
 

Related to Simple Harmonic Motion: Maximum Velocity and Acceleration Calculation

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line, with a constant amplitude and a constant period. This type of motion is caused by a force that is directly proportional to the displacement of the object from its equilibrium position.

What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x(t) = A sin(ωt + φ), where x is the displacement of the object, A is the amplitude, ω is the angular frequency, and φ is the phase angle. This equation describes the position of the object at any given time.

What is the difference between simple harmonic motion and damped harmonic motion?

Simple harmonic motion is a type of motion that does not experience any external forces or friction, while damped harmonic motion is a type of motion that experiences forces such as friction that cause the amplitude of the motion to decrease over time. Damped harmonic motion also has a different equation, taking into account the damping coefficient.

How is simple harmonic motion related to energy?

Simple harmonic motion is related to energy through the conservation of energy principle. As the object in simple harmonic motion moves back and forth, it experiences potential energy and kinetic energy. The total mechanical energy (potential + kinetic) remains constant throughout the motion, as long as there are no external forces acting on the object.

What are some examples of simple harmonic motion in everyday life?

Some examples of simple harmonic motion include a pendulum, a mass on a spring, and a rocking chair. Other examples include the vibration of a guitar string, the motion of a swing, and the motion of a diving board. Simple harmonic motion can also be observed in the motion of atoms and molecules in a solid or liquid.

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