Question

Q4 [LQ] For a horizontal damped spring-mass system with parameters, mass = m, spring constant = k, and drag coefficient = b, is subject to a driving force given by F₀cos(ωt). Show that, for t ≫ 1/β, the time average over a period τ = 2π/ω of the kinetic energy of the system (T) = (1/τ)∫₀^(τ) (1/2)mẋ²dt is maximum when the driving frequency ω = ω₀ = √(k/m).

Name: q4 lq for a horizontal damped spring mass system with parameters mass m spring constant k and drag coefficient b is subject to a driving force given by f0cost show that for t 1 the time aver 71914
Uploaded: 2022-05-10T03:50:09-08:00
Duration: 4 min 33 s
Channel: Madhur L
Description: q4 lq for a horizontal damped spring mass system with parameters mass m spring constant k and drag coefficient b is subject to a driving force given by f0cost show that for t 1 the time aver 71914

          Q4 [LQ]
For a horizontal damped spring-mass system with parameters, mass = m, spring constant = k, and drag coefficient = b, is subject to a driving force given by F₀cos(ωt). Show that, for t ≫ 1/β, the time average over a period τ = 2π/ω of the kinetic energy of the system (T) = (1/τ)∫₀^(τ) (1/2)mẋ²dt is maximum when the driving frequency ω = ω₀ = √(k/m).

Added by Samantha B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

05/10/2022

Step 1

Step 1: The equation of motion for the damped spring-mass system with a driving force is given by: m*ẍ + b*ẋ + kx = F₀cos(ωt) where x is the displacement of the mass from its equilibrium position, ẋ is the velocity of the mass, ẍ is the acceleration of the Show more…

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Q4 [LQ] For a horizontal damped spring-mass system with parameters, mass = m, spring constant = k, and drag coefficient = b, is subject to a driving force given by F₀cos(ωt). Show that, for t ≫ 1/β, the time average over a period τ = 2π/ω of the kinetic energy of the system (T) = (1/τ)∫₀^(τ) (1/2)mẋ²dt is maximum when the driving frequency ω = ω₀ = √(k/m).