Question

could someone please help me with question 1d) in the attached photo

Answer 1

the function would be 1.5 + amplitude*sin(2*pi*t/T)
where T is the period.
what did you get for the amplitude and period?

Answer 2

i got 1.5 for the period and 0.5 for the amplitude.
but the answers tell me that the equation for the sinusoidal function is f(t)=-0.5cos(180t)˚+1.5

Answer 3

at first the equation I got was f(t) = 0.5sin(240x)+1.5
240 is the period since 2(pi)/k = period.
so, 2(pi)/1.5= 240.

Answer 4

240 since 2(pi) = 360

Answer 5

The period is the number of seconds to complete one wavelength. It looks like about 2 secs from the picture, but I can not make out the grid, so it may not be exactly 2 seconds.

If it were 2 seconds, then sin(2pi*t/2) = sin(pi*t) (in radians) or sin(180 t) would repeat every 2 seconds (t=2 would mean 180*2= 360 degrees)

Answer 6

OH ! my bad... yeah the period is 2.
sorry that's my mistake. i didn't realize that the wave started at 1.5
haha. alright that makes more sense.
hmm.. but i want to know, why do they use the cosine instead of sine?

Answer 7

good question. If we plug in t=0 into their answer
f(t)=-0.5cos(180t)˚+1.5
f(0)= 1.5 - 0.5*cos(0)= 1.5-0.5= 1.0
which says at t=0 we should see the curve at 1. But it is at 1.5
On the other hand, if we use sin:
1.5+0.5*sin(180*t)
we get 1.5 at t=0
at t= 0.5 we get 1.5+0.5*sin(90)= 2.0 which matches.

so their answer looks bogus to me.

Answer 8

alright. well I'm going to use the sine function because when i graph it as well, the graph does not even look like the graph that is given on the paper.
thank you for your help ! :)