A damped harmonic oscillator consists of a mass on a spring, with a small damping force that is proportional to the speed of the block. If the mass of the block is 320 g, the period of oscillation is 2.4 s, and the block loses 10% of its mechanical energy after one cycle, what is the damping constant?

2.19 N/m

Explanation:

A damped harmonic oscillator is formed by a mass in the spring, and it does a harmonic simple movement. The period of it is the time that it does one cycle, and it can be calculated by:

T = 2π√ (m/K)

Where T is the period, m is the mass (in kg), and K is the damping constant. So:

2.4 = 2π√ (0.320/K)

√ (0.320/K) = 2.4/2π

√ (0.320/K) = 0.38197

(√ (0.320/K)) ² = (0.38197) ²

0.320/K = 0.1459

K = 2.19 N/m