818 Critical Damping

Damped oscillations must return to the equilibrium position eventually as the damping force saps energy continously from the oscillation. However, the manner in which the oscillations cease depends on the degree of damping.

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In the video, critical damping was achieved when the aluminium block was 2.0 cm from the magnets (1:46). Under critical damping, the pendulum returned immediately to the equilibrium position in the shortest amount of time possible, without overshooting the equilibrium position.

With less damping than critical (underdamping or light damping), the pendulum overshoots the equilibrium position and oscillates around it. The amplitude of oscillation decays exponentially as the damping force withdraws energy from the pendulum.

With more damping than critical (overdamping or heavy damping), the pendulum also does not overshoot the equilibrium position, but returns to the equilibrium position more slowly.

The collage at the end of the video shows very clearly that critical damping brings the oscillator to rest in the shortest time.

Why is there a damping force?

As the magnet swings, the aluminium along side the magnet experiences first an increasing and then a decreasing flux linkage, resulting in induced emf. (E=/dt)

Since aluminium blocks are conductors, (eddy) currents formed in the blocks, producing their own magnetic field.

The polarity of the induced emf must be such as to produce a induced current and magnetic field that opposes the change that caused the induction in the first place. (Lenz’s Law). This predicts a retarding magnetic force on the pendulum that is always in opposite direction to the velocity of the pendulum, hence a damping force.

How is the degree of damping varied?

By moving the block closer to the magnets, the rate of change of magnetic flux linkage is increased, resulting in a larger induced emf, current and thus damping force.

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