Perturbation Theory: How Does Oscillation Amplitude Vary with Length?

[Nusc]

Homework Statement

The length of a pendulum is slowly doubled (l=l_0(1+epsilon*t), 0<=t<=1/epsilon). How does the amplitude q_max of the oscillations vary?

Any hints?

Homework Equations

The Attempt at a Solution

 

[chrispb]

Are you changing the total energy? By how much?

 

[Nusc]

I'm not sure...Ans. I = 1/2 * l^{3/2} * g^{1/2} *q_max^{2}.

therefore

q_max(t) = q_max(0)(l(0)/l(t))^3/4