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Problems
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Design an actively shielded gradient coil system for a 1.5 Tesla clinical MRI scanner. Calculate current requirements, inductance constraints, thermal dissipation, Lorentz forces, and verify compliance with IEC 60601-2-33 safety standards for peripheral nerve stimulation.

Design a grid-scale battery energy storage system to smooth solar PV output and provide frequency regulation. Calculate minimum capacity requirements, optimal operating strategy, degradation modeling, round-trip efficiency losses, and economic viability including levelized cost of storage.

Design a quantum dot single-photon source for quantum key distribution networks. Calculate energy levels, Purcell enhancement, radiative lifetimes, decoherence mechanisms, and system efficiency to achieve secure key rates over metropolitan fiber distances.

Calculate special and general relativistic time dilation effects on GPS satellite atomic clocks. Determine orbital velocity, Lorentz factor, gravitational time dilation, net clock drift, and the required pre-launch frequency offset to maintain system accuracy.

Design a suspension system for an off-road vehicle to safely traverse a 100mm obstacle while meeting passenger comfort limits. Calculate spring stiffness, damping coefficients, maximum safe velocity, and required suspension travel using quarter-car modeling principles.