Take the Laplace transform of the following initial value and
solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t
y(0)=0,y′(0)=0
Y(s)= ? Hint: write the right hand side in
terms of the Heaviside function. Now find the inverse transform to
find y(t). Use step(t-c) for the Heaviside function u(t−c) .
y(t)= ?
Consider the parametric equation of a curve:
x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π
Part (a): Find the Cartesian equation of the
curve by eliminating the parameter. Also, graph the curve and
indicate with an arrow the direction in which the curve is traced
as the parameter increases. Label any x and y intercepts.
Part(b): Find the point (x,y) on the curve with
tangent slope 1 and write the equation of the tangent line.