Question

The displacement d (in meters) of an object at time t (in seconds) is given.

d=-11sin(t/9)

a)what is the maximum displacement from its rest position?
b)What is the time required for one oscillation? Round your answer to two decimal places.

Answer 1

for
d=Asinwt
max displacement from rest position is given by A
and time period is T = 2(pi)/w...
can you proceed now..

Answer 2

so is A=-11
and w=1/9

Answer 3

Sine values of an angle is always between -1 and 1
so the Max will be when Sin(angle) = 1
so
d = -11 * 1 = -11 and you got that right in your answer above.

One oscillation of the Sin curve is from 0 to 2*pi , where pi = 180 degree and 2pi = 360
Here is a diagram


Based on the formula from @matricked above
the Time for one oscillation t = 2*pi /w = 2pi/(1/9) = 18pi in seconds = 56.55 sec