hemetite
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Qn4.
A damped harmonic oscillator involves a block of mass 2.0kg and a spring with a stiffness 10 N/m. The damping force is proportioanla to the velocity of the oscillator. Initially it osicillates with an amplitude of 25cm. Due to the damping, the amplitude fallsto three-fourth of this initial value after 4 complete cycles..
(a) What is the value of the damping constant?
(b) How much energy has been "dissipated" during the 4 cycles?
Here are my thoughts..
Initial A=0.25m
after 4 cycle it reduced to = 3/4 * 0.25 = 0.1875m
w=sqrt [ k/m - (b/2m)sq]
= sqrt [ 10/2 - (bsq)/16
= sqrt [(80-bsq) / 16 ]
i will be using
x(t) = A exp (-b/2m)t sin (wt + teta) -----------> equation 1
at t= 0 for the first cycle A= 0.25m
1 cycle = 2pi, after 4 complete cycle. it will be at 8pi
therefore putting the values A= 0.25, t=8pi, m=2kg and w= sqrt [(80-bsq) / 16 ]
into equation 1
0.1875= 0.25 exp (-b/4) 8pi sin (w8pi) * sqrt [(80-bsq) / 16 ]
here i solve for b...to get answer the first answer
am i on the right track?
A damped harmonic oscillator involves a block of mass 2.0kg and a spring with a stiffness 10 N/m. The damping force is proportioanla to the velocity of the oscillator. Initially it osicillates with an amplitude of 25cm. Due to the damping, the amplitude fallsto three-fourth of this initial value after 4 complete cycles..
(a) What is the value of the damping constant?
(b) How much energy has been "dissipated" during the 4 cycles?
Here are my thoughts..
Initial A=0.25m
after 4 cycle it reduced to = 3/4 * 0.25 = 0.1875m
w=sqrt [ k/m - (b/2m)sq]
= sqrt [ 10/2 - (bsq)/16
= sqrt [(80-bsq) / 16 ]
i will be using
x(t) = A exp (-b/2m)t sin (wt + teta) -----------> equation 1
at t= 0 for the first cycle A= 0.25m
1 cycle = 2pi, after 4 complete cycle. it will be at 8pi
therefore putting the values A= 0.25, t=8pi, m=2kg and w= sqrt [(80-bsq) / 16 ]
into equation 1
0.1875= 0.25 exp (-b/4) 8pi sin (w8pi) * sqrt [(80-bsq) / 16 ]
here i solve for b...to get answer the first answer
am i on the right track?