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A thin string is held at one end and osc...

A thin string is held at one end and oscillates so that,
`y(x = 0, t) = 8 sin 4t(cm)`
Neglect the gravitattional force. The dtring's linear mass density is `0 .2 kg// m` and its tension is ` 1 N`. The string passes through a bath filled with `1 kg` water. Due to friction heat is transferred to the bath. The heat transfer efficiency is `50%`. Calculate how much time passes before the temperature of the bath rises one degree kelvin?

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