Adamped harmonic oscillator consists of a mass on a spring, with a damping force proportional to the speed of the block. if the spring constant is 350 n/m, the mass of the block is 240 g, the damping constant is 0.41 kg/s, and the block is displaced 7.5 cm from its equilibrium position and then released, what is its kinetic energy after one cycle?

Explanation:

Given:

Now the frequency of damped oscillation is given as:

Now time period of one oscillation:

We know the equation of motion for the damped harmonic motion of a mass attached to a spring is given as:

........................(1)

From above we find the position of the mass:

is the position after 1 cycle.

So, the Kinetic energy can be given as: