Question

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)

Answer 1

The expression for the kinetic energy of the object as a function of time, t is $K.E = \frac{1}{2} k A^2 \ cos^2 \ (2\pi ft)$.

The general wave equation is given as;

$x = A \ cso(\omega t)\\\\x = A \ cos(2 \pi ft)$

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

$K.E = U_x\\\\K.E = \frac{1}{2} kx^2$

Substitute the value of x into the kinetic energy equation

$K.E = \frac{1}{2} kx^2\\\\K.E = \frac{1}{2} k ( A \ cos (2\pi ft)^2\\\\K.E = \frac{1}{2} k A^2 \ cos^2 \ (2\pi ft)$

Thus, the expression for the kinetic energy of the object as a function of time, t is $K.E = \frac{1}{2} k A^2 \ cos^2 \ (2\pi ft)$.

Learn more here:https://brainly.com/question/13736293