The question is to find a s function given by s(t) = a cos(ωt) that models the displacement of the weight.
Answer:
The function is given as:
s(t) = a cos(ωt)
This means that to get the exact function modelling the given situation, we will have to get values for ω and a.
1- getting the value of ω:
period = 0.8 sec
frequency = 1/period = 1/0.8 = 5/4 hz
ω = 2πf = 2*π*5/4 = 2.5π rad/sec
The function now became:
s(t) = a cos(2.5πt)
2- getting the value of a:
We are given that:
s(0) = 1 in
This means that:
s(t) = a cos(2.5πt)
1 = a cos(2.5π*0)
1 = a cos(0)
a = 1
Therefore, the function is:
s(t) = cos(2.5πt)
To get the value of the function at any instance (t), substitute with the value of "t" in the above function and get the corresponding s(t)
Hope this helps :)
