Question

A harmonic oscillator starts with an amplitude of 20.0 cm. After 10.0 s, the amplitude decreases to 15.0 cm. If the linear damping coefficient is 2.00 Ns/m, how much mass is oscillating

Answer 1

Answer: the amount of mass is oscillating is 34.8 kg

Step-by-step explanation:

Given that;

amplitude A = 20.0 cm

time t = 10 s

amplitude decreases x = 15.0 cm

damping coefficient b = 2.00 N.s/m

amount of mass is oscillating = ?

we know that; amplitude can be expressed as;

x = Ae^-(∝t)

we substitute

15 = 20e^-∝(10)

∝ = 0.02877 s⁻¹

Hence mass m will be;

m = b/2∝

we substitute

m = (2 N.s/m) / ( 2 × 0.02877 s⁻¹)

m = 34.8 kg

Therefore the amount of mass is oscillating is 34.8 kg