An electromagnetically maintained clock pendulum receives timed energy to replace its mechanical losses. This calculator shows a two-second pendulum and estimates the energy needed between ideal replenishments. The illustration separates the moving rod, bob and armature from the fixed support and coil.
Electro-magnetic Clock Pendulum Interactive Calculator
Watch a seconds pendulum and compare the mechanical energy lost between impulses. The corrected interval calculation retains all five controls and separates the ideal magnetic-gap comparison.
Equation Used
- Two-second small-angle period and point-mass bob.
- Constant weak-damping Q.
- Ideal replenishment restores the entered post-impulse energy.
- Separate gap comparison assumes fixed ampere-turns and gap-dominated reluctance.
Impulse output is mechanical energy, not electrical consumption. Gap-force ratio is a separate ideal comparison.
Free swing and periodic replenishment
The bob swings about its suspension under gravity. Mechanical loss reduces its energy between impulses. A correctly timed electromagnetic drive adds energy near a suitable crossing so the motion can continue.
The drawing uses the opposed horizontal electromagnets and pivoted armature principle shown in US1132012A. It simplifies the frame and omits the patent’s contact mechanism and clock train. Actual electrical clocks use different contact, sensing, magnetic and counting arrangements. A fixed interval in this model should not be confused with an amplitude-triggered Hipp toggle or a gravity impulse mechanism.
The visual uses the entered angle without increasing it: precision pendulums have small swings. The pole clearance alone is enlarged to make it visible. Playback follows the nominal two-second period, and the cycle slider covers one entered replenishment interval.
Compare the energy requirement
Mass and peak angle determine stored energy. Quality factor and elapsed time determine the modeled loss. The impulse result is mechanical energy to restore that loss, not electrical energy drawn from a battery.
The pole-gap input is retained as a separate ideal comparison at fixed ampere-turns. It does not change how much mechanical energy the pendulum loses. The calculator cannot infer pulse current or duration from gap alone.
Energy loss over the full interval
With gravitational acceleration g=9.80665 m/s² and small-angle period T=2 s, effective length is L=g(T/2π)², approximately 0.9936 m. At peak angle θ, stored energy is E=mgL(1−cos θ).
For a lightly damped oscillator of quality factor Q, the energy envelope decays as E(t)=E exp(−2πt/(QT)). The ideal mechanical replenishment after interval Δt is therefore ΔE=E[1−exp(−2πΔt/(QT))]. For small losses this is approximately 2πEΔt/(QT).
There are Δt/T complete oscillations, or 2Δt/T half-swings, in the interval. Increasing the interval increases energy lost; the previous expression incorrectly divided the loss by the interval.
The separate gap comparison is 100(0.5 mm / gap)² percent. It assumes an ideal gap-dominated magnetic circuit with fixed ampere-turns, area and negligible leakage, fringing and saturation. It is not a universal force law for an arbitrary clock coil.
Changing the interval
With all other inputs fixed, a 60-second wait needs more replenishment energy than a 30-second wait. The increase is nearly twofold for high Q, with the exact exponential accounting for the gradually decreasing energy during decay.
Doubling mass doubles both stored and replenishment energy. Increasing Q reduces the required replenishment. Increasing the gap from 0.5 to 1 mm makes the separate ideal fixed-current force comparison 25%; it does not reduce the mechanical energy that the pendulum must regain.
Limits of this pendulum model
The fixed effective length treats the bob as a point mass on a massless rod. Finite-angle period correction, distributed rod inertia, temperature, suspension compliance and clock-train loading are omitted. The entered Q represents weak damping and is assumed constant.
Mechanical replenishment is not coil electrical consumption. Copper loss, driver loss and magnetic conversion efficiency are absent. The drive cue is not a prescribed pulse duration, coil design or claim of timekeeping accuracy.
Real impulse timing affects both amplitude and rate. No universal gap tolerance, pulse energy or daily accuracy is inferred here.
Pendulum questions
Why is the movement so small?
The allowed angles are 0.5° to 4°, shown honestly on the drawing. Larger drawn swings would misrepresent the input.
Why does more time between impulses require more energy?
More damping loss accumulates before replenishment. The result integrates that interval rather than dividing by it.
Is the impulse result a battery requirement?
No. It is mechanical energy delivered to the pendulum; electrical input would be larger and depends on the drive.
Why does pole gap not change stored energy?
Pendulum energy depends on mass, effective length and angle. Gap belongs to the separate magnetic-force comparison.
References
- US1132012A: Electric pendulum clock — opposed electromagnets, pivoted armature and pendulum-controlled contacts; basis for the simplified magnetic layout.
- University of Texas: Quality Factor — weakly damped oscillator energy loss per cycle.
- MIT: Magnetic Circuits and the Air Gap Field of an Electromagnet — ideal magnetic-circuit assumptions.
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