the displacement, y(m), of a body in damped oscillation is y = 2e^-t sin3t. use the product rule to find an equation for the object if y = dy/dt.

Answer 1

Hi,

y = 2e^-t sin3t your mean is y = 2e^-t * sin3t

If yes, you know the product rule is (u.v)' = u' v + uv'

in this case u = 2e^-t and v= sin3t

now u' = -2 e^-t and v' = 3 cos3t

y = dy/dt = -2 e^-t * sin3t + 2e^-t *3 cos3t

It is better you simplify! by factoring of 2e^-t

y = dy/dt = 2e^-t( - sin3t + 3 cos3t)

I hope it is useful,

Minoo