Test Questions on Force-Voltage and Force-Current Analogies in DEs

📚 Quick Study Guide

• 🍎 In the Force-Voltage analogy (also called the direct analogy), force is analogous to voltage, mass is analogous to inductance, damping coefficient is analogous to resistance, and displacement is analogous to charge.
• 💡 The relationships are as follows:
  • $F \leftrightarrow V$ (Force corresponds to Voltage)
  • $m \leftrightarrow L$ (Mass corresponds to Inductance)
  • $b \leftrightarrow R$ (Damping coefficient corresponds to Resistance)
  • $k \leftrightarrow \frac{1}{C}$ (Spring constant corresponds to Inverse Capacitance)
  • $x \leftrightarrow q$ (Displacement corresponds to Charge)
• 🧪 In the Force-Current analogy (also called the inverse analogy), force is analogous to current, mass is analogous to capacitance, damping coefficient is analogous to conductance, and displacement is analogous to flux linkage.
• 📝 The relationships are as follows:
  • $F \leftrightarrow I$ (Force corresponds to Current)
  • $m \leftrightarrow C$ (Mass corresponds to Capacitance)
  • $b \leftrightarrow \frac{1}{R}$ (Damping coefficient corresponds to Inverse Resistance or Conductance)
  • $k \leftrightarrow \frac{1}{L}$ (Spring constant corresponds to Inverse Inductance)
  • $v \leftrightarrow V$ (Velocity corresponds to Voltage)
• 🔑 Understanding these analogies helps in analyzing mechanical systems using electrical circuit analysis techniques and vice-versa.
• 🧭 Remember that choosing the correct analogy depends on the specific problem and what quantities you want to relate.

Practice Quiz

1. Which electrical element is analogous to mass in the Force-Voltage analogy?
   1. A. Resistor
   2. B. Capacitor
   3. C. Inductor
   4. D. Voltage Source
2. In the Force-Current analogy, what electrical quantity is analogous to the damping coefficient?
   1. A. Resistance
   2. B. Capacitance
   3. C. Inductance
   4. D. Conductance
3. If force is analogous to voltage, displacement is analogous to charge, then stiffness is analogous to which quantity?
   1. A. Capacitance
   2. B. Inverse Capacitance
   3. C. Inductance
   4. D. Resistance
4. Which of the following is true for the Force-Voltage analogy?
   1. A. Velocity corresponds to current
   2. B. Displacement corresponds to flux
   3. C. Force corresponds to current
   4. D. Force corresponds to voltage
5. In the Force-Current analogy, what is analogous to velocity?
   1. A. Current
   2. B. Voltage
   3. C. Charge
   4. D. Flux Linkage
6. What electrical element corresponds to the spring constant in the Force-Current analogy?
   1. A. Resistor
   2. B. Capacitor
   3. C. Inverse Inductance
   4. D. Inductance
7. Which of the following mechanical quantities is analogous to current in the Force-Current analogy?
   1. A. Force
   2. B. Displacement
   3. C. Velocity
   4. D. Acceleration