Simple Harmonic Motion(SHM) - Force, Acceleration, & Velocity at 3 Positions

Summary

This video discusses the core principles of simple harmonic motion (SHM) using a mass-spring system. It explores how velocity, acceleration, and spring force vary at different positions. At positions 1 and 3 (maximum displacement), velocity is zero, while at position 2 (equilibrium), velocity is maximized. The spring force is strongest at the extremes, with acceleration following a similar pattern. The video also emphasizes that SHM is not uniformly accelerated motion, meaning the equations for uniformly accelerated motion don’t apply. This explanation clarifies key SHM concepts for a deeper understanding of motion dynamics.

Takeaways

• 😀 The positions in simple harmonic motion are defined as: positions 1 and 3 at maximum displacement, and position 2 at the equilibrium position.
• 😀 The velocity at positions 1 and 3 is zero because the mass changes direction there, just like the velocity of an object in freefall is zero at the top of its path.
• 😀 The velocity at position 2 is at its maximum magnitude because the mass is moving through the equilibrium position.
• 😀 The spring force follows Hooke’s Law: the force is proportional to the displacement from equilibrium, and is greatest at positions 1 and 3.
• 😀 At position 2 (equilibrium position), the spring force is zero because the displacement is zero.
• 😀 The maximum displacement from equilibrium is called the amplitude of the simple harmonic motion.
• 😀 The acceleration of the mass is directly proportional to the spring force, meaning it is maximum at positions 1 and 3 and zero at position 2.
• 😀 At positions 1 and 3, both the spring force and acceleration are at their maximum, while at position 2, both are zero.
• 😀 The changing spring force accelerates the mass towards the equilibrium position, which means the mass speeds up as it moves towards it and slows down when moving away.
• 😀 Simple harmonic motion is not uniformly accelerated motion because the acceleration is not constant throughout the motion.

Q & A

What are the three key positions in simple harmonic motion (SHM) for a mass-spring system?

The three key positions in SHM are: Position 1 and Position 3, where the mass is at maximum displacement from the equilibrium (on either side); and Position 2, where the mass is at rest (equilibrium position).

Why is the velocity zero at positions 1 and 3 in simple harmonic motion?

The velocity is zero at positions 1 and 3 because the mass changes direction at these points, which is similar to the vertical velocity of an object in free fall being zero at the top of its path.

Where is the velocity of the mass greatest in a simple harmonic motion system?

The velocity is greatest at position 2, the equilibrium position, because this is where the displacement is zero, and the mass is moving fastest.

How does Hooke’s Law relate to the spring force in simple harmonic motion?

According to Hooke’s Law, the spring force is proportional to the displacement from the equilibrium position, given by the equation F = -kx, where k is the spring constant and x is the displacement.

What is the magnitude of the spring force at positions 1 and 3 in SHM?

The magnitude of the spring force is at its maximum at positions 1 and 3 because the displacement from equilibrium is maximum at these points.

What is the relationship between spring force and acceleration in SHM?

The spring force is directly proportional to the acceleration in SHM. According to Newton's Second Law (F = ma), since the spring force is proportional to displacement, the acceleration follows the same pattern, with maximum acceleration at positions 1 and 3.

At which position is the spring force zero in simple harmonic motion?

The spring force is zero at position 2 (the equilibrium position), where the displacement from equilibrium is zero.

What is the amplitude in simple harmonic motion?

The amplitude is the maximum displacement from the equilibrium position, which occurs at positions 1 and 3 in SHM.

Why is the velocity at position 2 the maximum in SHM?

The velocity at position 2 is maximum because the mass is passing through the equilibrium position, where the spring force accelerates the mass toward equilibrium, leading to the highest velocity.

Is simple harmonic motion uniformly accelerated motion? Why or why not?

No, simple harmonic motion is not uniformly accelerated. The acceleration is not constant and varies depending on the displacement, so the equations for uniformly accelerated motion cannot be used in SHM.