A 1.0-kg mass oscillates along the x axis with simple harmonic motion. Its position as a function of time is given by X = 2 cos( $\pi$ t/6 + $\pi$ /3)
Where the units are SI. When t = 2 s, the kinetic energy of the mass is

Question

A 1.0-kg mass oscillates along the x axis with simple harmonic motion. Its position as a function of time is given by X = 2 cos(

\pi

t/6 +

\pi

/3)
Where the units are SI. When t = 2 s, the kinetic energy of the mass is

Quizplus · Accepted Answer

The kinetic energy of the mass is given by:$$K = \frac{1}{2}mv^2 = \frac{1}{2}m\left(\frac{dx}{dt}\right)^2$$where $m$ is the mass, $v$ is the velocity, and $x$ is the position.The velocity is given by the derivative of the position with respect to time:$$\frac{dx}{dt} = -2\pi f \sin(2\pi ft + \pi/3)$$where $f$ is the frequency of the oscillation.At $t = 2 s$, the velocity is:$$\frac{dx}{dt} = -2\pi f \sin(2\pi f(2) + \pi/3) = -2\pi f \sin(4\pi f + \pi/3)$$The kinetic energy is then:$$K = \frac{1}{2}m\left(\frac{dx}{dt}\right)^2 = \frac{1}{2}(1 kg)\left(-2\pi f \sin(4\pi f + \pi/3)\right)^2 = \frac{1}{2}\pi^2 f^2 \sin^2(4\pi f + \pi/3)$$The frequency of the oscillation is given by:$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$where $k$ is the spring constant.The spring constant is not given in the problem, so we cannot calculate the exact value of the kinetic energy. However, we can see that the kinetic energy is proportional to $\pi^2 f^2$. Therefore, the correct answer is the choice that has the highest value of $\pi^2 f^2$.The only choice that has the highest value of $\pi^2 f^2$ is A. Therefore, the correct answer is A.

A 10-Kg Mass Oscillates Along the X Axis with Simple Harmonic