Photo AI
Describe the movement of a particle that is undergoing simple harmonic motion. - Leaving Cert Physics - Question b - 2015
Question b
Describe the movement of a particle that is undergoing simple harmonic motion.
Worked Solution & Example Answer:Describe the movement of a particle that is undergoing simple harmonic motion. - Leaving Cert Physics - Question b - 2015
Step 1
Acceleration is proportional to
Answer
In simple harmonic motion (SHM), the acceleration of the particle is always directed towards the equilibrium position. This is mathematically represented as:
a = - rac{k}{m} x
where:
- ( a ) is the acceleration,
- ( k ) is the force constant,
- ( m ) is the mass of the particle,
- ( x ) is the displacement from the equilibrium position.
This shows that the acceleration is proportional to the negative of the displacement, indicating that the force acting on the particle also tends to restore it towards the equilibrium position.
Step 2
Displacement (from a point on the path)
Answer
The displacement of the particle undergoing simple harmonic motion can be described using the formula:
where:
- ( x(t) ) is the displacement at time ( t ),
- ( A ) is the maximum amplitude of the motion,
- ( \theta = \omega t + \phi ), where ( \omega ) is the angular frequency,
- ( \phi ) is the phase constant.
The particle oscillates around the equilibrium position, moving back and forth through the maximum amplitude, and this periodic motion reflects the characteristics of SHM.