MathDB

8

Part of 2017 Korea USCM

Problems(1)

damping oscillators

Source: 2017 South Korea USCM P8

8/15/2020
u(t)u(t) is solution of the following initial value problem. {u′′(t)+u′(t)=sin⁡u(t)    (t>0),u(0)=1,    u′(0)=0\begin{cases} u''(t) + u'(t) = \sin u(t) &\;\;(t>0),\\ u(0)=1,\;\; u'(0)=0 & \end{cases} (1) Show that u(t)u(t) and u′(t)u'(t) are bounded on t>0t>0. (2) Find lim⁡t→∞u(t)\lim\limits_{t\to\infty} u(t) with proof.
differential equationordinary differential equationcollege conteststrigonometry