stunner5000pt
Mar24-05, 12:03 PM
A mass M is suspended fro mtwo springs attached in series as shown in the diagram. The system is hanging in the gravitational field of earth. One spring has the spring constant k1 and the other is k2. Mass of springs is neglacted. Fin the period T of the SHM
m \frac{d^2 y}{dt^2} + (k_{1}+k_{2}) y = mg
and of course the solution to the homogenous equation is
Y(t) = e^{i \frac{\sqrt{k_{eff}}}{m} t}
and if i guess the soltuion to the non homogenous equation to be
y(t) = \frac{1}{- \omega^2 + i \omega} cos \omega t
so the full soltuion becomes Y(t) = e^{i \frac{\sqrt{k_{eff}}}{m} t} + \frac{1}{- \omega^2 + i \omega} cos \omega t
but how do i find the period T
seems like i have gona on a tangent of sorts, have i over-solved the problem??
m \frac{d^2 y}{dt^2} + (k_{1}+k_{2}) y = mg
and of course the solution to the homogenous equation is
Y(t) = e^{i \frac{\sqrt{k_{eff}}}{m} t}
and if i guess the soltuion to the non homogenous equation to be
y(t) = \frac{1}{- \omega^2 + i \omega} cos \omega t
so the full soltuion becomes Y(t) = e^{i \frac{\sqrt{k_{eff}}}{m} t} + \frac{1}{- \omega^2 + i \omega} cos \omega t
but how do i find the period T
seems like i have gona on a tangent of sorts, have i over-solved the problem??