1. A damped harmonic oscillator is driven by a sinusoidal force f(t) = focos wt: dx dt d²x m +b +kx=fo cos wt. dt2 At t1/, displacement x(t) of the point mass of the oscillator is where fo x(t) 1 m [(ww²)²+4y²w²] 1/2 k b ωο Υ and cos M 2m' sin(wt), 2γω - [(ww²)2 + 472w2] 1/2* (1) (1) Find the work done by the sinusoidal force on m in one period of the oscillation. (2) Find the work done by the damping force -bv on m in one period of the oscillation.
1. A damped harmonic oscillator is driven by a sinusoidal force f(t) = focos wt: dx dt d²x m +b +kx=fo cos wt. dt2 At t1/, displacement x(t) of the point mass of the oscillator is where fo x(t) 1 m [(ww²)²+4y²w²] 1/2 k b ωο Υ and cos M 2m' sin(wt), 2γω - [(ww²)2 + 472w2] 1/2* (1) (1) Find the work done by the sinusoidal force on m in one period of the oscillation. (2) Find the work done by the damping force -bv on m in one period of the oscillation.
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![1. A damped harmonic oscillator is driven by a sinusoidal force f(t) = focos wt:
dx
dt
d²x
m +b +kx=fo cos wt.
dt2
At t1/, displacement x(t) of the point mass of the oscillator is
where
fo
x(t)
1
m [(ww²)²+4y²w²] 1/2
k
b
ωο
Υ
and cos
M
2m'
sin(wt),
2γω
-
[(ww²)2 + 472w2] 1/2*
(1)
(1) Find the work done by the sinusoidal force on m in one period of the oscillation.
(2) Find the work done by the damping force -bv on m in one period of the oscillation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff31f1a0d-7853-4e11-9385-e0635d52ca16%2F93375b88-1361-4167-a13c-230da53b608a%2Fkif9v9u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A damped harmonic oscillator is driven by a sinusoidal force f(t) = focos wt:
dx
dt
d²x
m +b +kx=fo cos wt.
dt2
At t1/, displacement x(t) of the point mass of the oscillator is
where
fo
x(t)
1
m [(ww²)²+4y²w²] 1/2
k
b
ωο
Υ
and cos
M
2m'
sin(wt),
2γω
-
[(ww²)2 + 472w2] 1/2*
(1)
(1) Find the work done by the sinusoidal force on m in one period of the oscillation.
(2) Find the work done by the damping force -bv on m in one period of the oscillation.
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