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

d²x/dt² - 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)