In the limit of weak damping ( γ/ω << 1) and small angles, show that the total energy (sum of kinetic and potential energy) of a pendulum described by equations x(t) = x0e^−γt/2 cos (ωrt + α) and v(t) = −x0ωe^−γt/2 sin(ωrt + α) is constant over one period, but decays in time proportional to e−γt .
In the limit of weak damping ( γ/ω &lt;&lt; 1) and small
angles, show that the total energy (sum of kinetic and potential energy) of a pendulum described by equations x(t) = x0e^−γt/2 cos (ωrt + α) and v(t) = −x0ωe^−γt/2 sin(ωrt + α) is constant over one period, but decays in time proportional to e−γt .
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