(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Spring – mass system with spring constant k = 40 N/m and mass 10 kg.

a. Find the angular speed and period. Draw the response X versus time t

b. Linear damping is added with ζ = 4 %. Find the angular speed and period. Draw the response

c. Viscous damping is added with c_{1}= 0.03. Find the angular speed and period. Draw the response

d. Another viscous damping with c_{2}= 0.015 added parallel to c_{1}. Find the angular speed and period

e. If a force F = F_{0}cos (2.3t) is applied to the system, will it be closer to the resonance, undamped system or system with viscous damping?

f. The spring is divided into 4 parts of equal length and arranged as follows.

Find the angular speed and period of the system.

g. 2 viscous damper are added into the above system in series between point B and C with damping coefficient c_{1}= 0.03 and c_{2}= 0.02. Find the period and angular speed of this system

2. Relevant equations

k_{series}= k_{1}+ k_{2}

1/k_{parallel}= 1/k_{1}+ 1/k_{2}

k' = (1 - ζ )k

[tex]ω'=ω_o \sqrt{1-(\frac{c}{2m})^2}[/tex]

ω = √(k/m)

ω = 2π/T

3. The attempt at a solution

OK actually my teacher didn't teach anything in class. Only gave formula and homework, so I am just trying to use the formula without understanding the concept here because the test is tomorrow. Please excuse my poor understanding and for now I haven't drawn the response graph because I really don't understand how

a. ω = √(k/m) = √(40/10) = 2 rad/s

ω = 2π/T

T = π s

b. k' = (1 - ζ )k = (1 - 0.04) . 40 = 38.4 N/m

ω = √(k'/m) = 1.96 rad/s

T = 2π/ω = 3.2 s

c. [tex]ω'=ω_o \sqrt{1-(\frac{c}{2m})^2}[/tex]

ω' = 2 √(1-(0.03/20)^{2}) ≈ 1.99 rad/s

T = 2π/ω = 3.14 s

d. c = c_{1}+ c_{2}= 0.04

[tex]ω'=ω_o \sqrt{1-(\frac{c}{2m})^2}[/tex]

ω' ≈ 1.99 rad/s

T = 2π/ω = 3.14 s

e. no clue at all

f. because k is inversely proportional to length and the spring is divided into 4 parts, so the value of k for each part is 160 N/m

After some calculation, k_{total}= 400 N/m

ω = √(k'/m) = 2√10 rad/s

T = 2π/ω = 0.99 s

g. do not understand at all

I am not sure whether my work right or wrong...

Thanks

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# Oscillation with damping

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