Working out velocity of particle moving in SHM

In summary, the velocity of a particle in Simple Harmonic Motion (SHM) can be calculated using the formula v = -ωA sin(ωt). The velocity is directly proportional to the displacement and can be negative if the particle is moving in the opposite direction of the equilibrium position. Factors such as amplitude, angular frequency, and mass can affect the velocity, and it changes sinusoidally over time in SHM.
  • #1
Bolter
262
31
Homework Statement
Calculate the velocity of a particle moving in SHM at a point
Relevant Equations
a = –w^2x
Screenshot 2020-02-25 at 17.46.51.png


So the way I have gone about it is to assume that the equilibrium position is half way between the 2 end points, hence the amplitude of this motion is 9.3/2 = 4.65 cm

Therefore the displacement of the particle when it is 2cm away from one end point should be the distance between that point and the equilibrium position. So i.e. 4.65 – 2 = 2.65 cm

Knowing those 2 values I have done this

IMG_3990.JPG


Is a speed of 0.16 m/s be what you should get?

Thanks for any help!
 
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  • #2
Looks about right.
 
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Likes Bolter

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion (SHM) is a type of periodic motion in which a particle moves back and forth along a straight line, with a constant amplitude and a frequency that remains the same over time. It is often seen in systems that have a restoring force, such as a mass attached to a spring.

2. How is the velocity of a particle in SHM calculated?

The velocity of a particle in SHM can be calculated using the formula v = ωAcos(ωt + φ), where v is the velocity, ω is the angular frequency, A is the amplitude, t is time, and φ is the phase constant. This formula takes into account the sinusoidal nature of SHM and the position of the particle at a given time.

3. What factors affect the velocity of a particle in SHM?

The velocity of a particle in SHM is affected by the amplitude, frequency, and phase of the motion. An increase in the amplitude will result in a higher maximum velocity, while a higher frequency will result in a faster oscillation and therefore a higher average velocity. The phase also plays a role in determining the velocity at a specific time.

4. Can the velocity of a particle in SHM be negative?

Yes, the velocity of a particle in SHM can be negative. This occurs when the particle is moving in the opposite direction of its initial displacement. In SHM, the velocity is constantly changing between positive and negative values as the particle moves back and forth.

5. How does the velocity of a particle in SHM relate to its acceleration?

The acceleration of a particle in SHM is directly proportional to its displacement from equilibrium and is in the opposite direction of the displacement. This means that when the particle is at its maximum displacement, the acceleration is at its maximum, and when the particle is at equilibrium, the acceleration is zero. The velocity of the particle is also related to its acceleration through the formula a = -ω²x, where a is the acceleration, ω is the angular frequency, and x is the displacement from equilibrium.

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