Step 1: Recall the equation for mechanical oscillations of a block-spring system
The equation of motion for a simple harmonic oscillator (block-spring system) is given by:
where:
is the mass of the block
is the displacement from equilibrium position
is the force constant of the spring
Step 2: Recall the equation for LC oscillations in an electrical circuit
For an ideal LC circuit (ignoring resistance), the voltage across the capacitor plus the voltage across the inductor must be zero, based on Kirchhoff's Voltage Law.
Voltage across capacitor:
Voltage across inductor (induced emf):
Setting the sum of voltages to zero (ignoring sign conventions for now for analogy):
Step 3: Compare the equations for mechanical and LC oscillations
Comparing the mechanical oscillation equation:
and the LC oscillation equation:
We can observe the following analogies between the physical quantities:
Displacement ( ) in mechanical system is analogous to Charge ( ) in electrical system.
Mass ( ) in mechanical system is analogous to Inductance ( ) in electrical system.
Force constant ( ) in mechanical system is analogous to in electrical system.
Step 4: Identify the electrical equivalent of the force constant
From the analogy in Step 3, the electrical equivalent of the force constant ( ) of the spring is , which is the reciprocal of capacitance.
Step 5: Check the options against the derived equivalent
Reciprocal of capacitive reactance: Capacitive reactance . Reciprocal is . This is frequency dependent and not a constant equivalent to .
Capacitive reactance: . Frequency dependent, not a constant equivalent to .
Reciprocal of capacitance: . This matches our derived equivalent.
Capacitance: . This is analogous to the reciprocal of the force constant (if we consider stiffness as reciprocal of force constant).
Step 6: Select the correct option
Based on the analogy derived, the electrical equivalent of the force constant of the spring is the reciprocal of capacitance.
Final Answer: The final answer is reciprocal of capacitance