Question

This problem requires a familiarity with the di erential
equations that model the mass spring-

oscillator system.

Suppose that a weight is attached to a spring and the resulting
motion has a period of 3 seconds.

At some point in time, another 2 kilograms are added to the weight
and the period becomes 4

seconds. Assuming that we have a frictionless system, nd the
initial mass that was attached

to the spring before the extra was added.

Answer #1

Fnet = ma = Kx

a = K/m x

d^{2}x/dt^{2} - K/m x =0

The solution of this equation is

x = C1cos K/mt + c2sin K/mt...............1

If two kilogram of mass is attached then the equation will become

x = C1 cos( K/ m +2) t + C2 sin (K/ m+2) t............2

Equation 1 is the equation of spring before mass is added and equ2 is the equation of the spring after mass is added.

The formula of angular frequancy for equ 1

w1 =(
K/m)^{1/2}

^{ The formula of
angular frequancy for equa 2}

^{
} w2 = K/
(m+2)

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Group of answer choices
increases
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not enough information
decreases
Flag this Question
Question 2
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