A linear harmonic oscillator is subjected to a periodic force such that it's amplitude is maximum at an angular frequency of 10 rad/s. What is the phase difference between applied force and it&#0

Question

A linear harmonic oscillator is subjected to a periodic force such that it's amplitude is maximum at an angular frequency of 10 rad/s. What is the phase difference between applied force and it's velocity at this frequency ? It's damping coefficient is 0.1 / sec. Fill the value of ∣ cot ϕ ∣ .

TestHub · Accepted Answer

​ tan ϕ = R ω L − ω C 1 ​ ​ = ω RC ω 2 LC − 1 ​ ​ ω = ω 0 2 ​ − 2 r 2 ​ = LC 1 ​ − 2 L 2 R 2 ​ ​ ​ tan ϕ = ω RC ω 2 LC − 1 ​ = − ω RC 2 L R 2 C ​ ​ = − 2 L ω R ​ ​ 2 L R ​ = r ​ tan ϕ = − ω r ​ ​ tan ϕ = − 10 0.1 ​ = 0.1 = 0.01 ​ cot ϕ = 100 ​

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