Question: suppose that g(t) is a twice differentiable function on [0,infinity) such that g(t), g'(t), and g''(t) all have Laplace transforms defined for s>0. Also suppose

suppose that g(t) is a twice differentiable function on [0,infinity) such that g(t), g'(t), and g''(t) all have Laplace transforms defined for s>0. Also suppose that L{g(t)}(s)=sin(1/s), g(0)=1, g'(0)=0. Based on this information, evaluate the following Laplace transform. L{e^-pit g(t)}(s)=

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