A door closer is engineered so that the door swings shut as quickly as possible without bouncing or oscillating. Which damping regime describes this behavior?
AUnderdamped
BCritically damped
COverdamped
DUndamped
Critical damping produces the fastest return to equilibrium without any oscillation. Underdamped systems oscillate (the door would bounce). Overdamped systems return without oscillating but more slowly than critically damped. Door closers and galvanometers are engineered to be critically damped for exactly this reason.
Question 2 True / False
Increasing the damping coefficient of an oscillator generally makes it return to equilibrium faster.
TTrue
FFalse
Answer: False
Critical damping is the optimal point — it produces the fastest return without oscillation. Adding damping beyond the critical value produces an overdamped system, which returns to equilibrium more slowly. So increasing damping helps only up to the critical threshold; beyond that, it makes the system sluggish.
Question 3 Short Answer
How does the presence of damping affect the oscillation frequency of an underdamped oscillator compared to the undamped natural frequency ω₀?
Think about your answer, then reveal below.
Model answer: Damping reduces the oscillation frequency. The damped frequency ω_d = √(ω₀² − (b/2m)²) is always less than the undamped natural frequency ω₀.
This follows from solving the characteristic equation of the damped oscillator ODE. The complex roots have an imaginary part ω_d that is smaller than ω₀ by an amount depending on the damping coefficient b. Physically, the system is losing energy on every cycle, which effectively slows the oscillation compared to the frictionless case.