[limetang]

There is a damped pendulum where the variation of theta is given by.

Theta= ae^(-kt/2) ( cos(w1t) + (k/2w1)*sin(w1t) )

Find A(t) and delta where

theta = A(t)cos(w1t -(delta) )

I mean I tried expanding cos to be A(t) ( cos(delta)*cos(w1t) + sin(delta)*sin(w1t) )

But now I'm a bit stuck as to where to go.

[steve10]

Compare what you expanded with the first equation you wrote down.

[limetang]

So A(t) = ae^(-kt/2)

and sin(delta)=K/2w1

and cos(delta)= 1

Which doesn't seem to work.

As it suggests that delta=0 which implies that sin(0)=K/2w1 which means that k=0 which can't be true.

[steve10]

you should have

A(t).cos(delta) = ae^(-kt/2)
and
A(t).sin(delta)= ae^(-kt/2).(k/2)w1