An object on the end of a spring with spring constant k moves in simple harmonic motion with amplitude A and frequency f. Which of the following is a possible expression for the kinetic energy of the object as a function of time t? a. kA^2sin^(2πft)
b. 1/2kA^2cos^2(2πft)
c. 1/2kA sin(2πft)
d. kAcos(2πft)
e. 1/2kAsin(2πft)

The expression for the kinetic energy of the object as a function of time, t is .

The general wave equation is given as;

Apply the principle of conservation of energy, the kinetic energy of a particle in such motion is given as;

Substitute the value of x into the kinetic energy equation

Thus, the expression for the kinetic energy of the object as a function of time, t is .

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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.

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!