Question

If y = 5sin (3t omega + alpha), find dy/dt if el omega and alpha are constant

Answer 1

Let omega = w

and, alpha = a

Thus,

y = 5sin(3t omega + alpha)

y = 5sin(3tw + a)

Differentiate y with respect to t,

dy/dt = 5[sin(3tw+a)]'

= 5[cos(3tw+a)]×(3tw+a)'

= 5[cos(3tw+a)]×3w

= 15w.Cos(3tw+a)

= 15omega×Cos(3t omega + alpha)