Answer: option b.
Explanation:
The kinetic energy of a spring with constant K is calculated as:
kinetic energy = (k/2)*x^2
Where x^2 is the displacement of the spring with respect to it's rest position.
This can be written as a function like:
x = A*cos(2*pi*f*t)
where:
A is the amplitude (the maximum distance that the spring can move in each direction)
f is the frequency (and 2*pi*f is the angular frequency)
and t is the variable, it represents the time.
Replacing this in the kinetic energy equation, we get:
kinetic energy = (k/2)*(A*cos(2*pi*f*t))^2
This is the same as the option b: b. 1/2kA^2cos^2(2πft)
Then the corrrect option is b.
