- #1

gmmstr827

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## Homework Statement

A 0.835-kg block oscillates on the end of a spring whose spring constant is k = 41.0 N/m. The mass moves in a fluid which offers a resistive force F = -bv, where b = 0.662 Ns/m.

a) What is the period of the motion?

b) What is the fractional decrease in amplitude per cycle?

c) Write the displacement as a function of time if at t = 0, x = 0, and t = 1.00 s, x = 0.120m.

m = 0.835 kg

k = 41.0 N/m

b = 0.662 Ns/m

g = -9.80 m/s^2

## Homework Equations

F = -bv

T (period) = 2*π*√(m/k)

ε = √(k/m) = √(g/l)

l = length

## The Attempt at a Solution

a) Since l is not given, I found it, since ε = √(k/m) and ε = √(g/l), therefore √(k/m) = √(g/l)

and l = .1996 m after plugging in the givens and solving for l.

Now, the rest I'm not as sure of:

F = -b*v = -(0.662 Ns/m)(-9.8 m/s^2) ≈ 6.49 N/s

So, using that value in place of g:

T (period) = 2π√(.1996m/6.49N/s) ≈ 1.102 s

^^^ Is that correct? How would I solve for b and c?