A 0.25 kg harmonic oscillator has a total mechanical energy of 6.5 J. If the osc

Question

A 0.25 kg harmonic oscillator has a total mechanical energy of 6.5 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency? A) None of the choices B) 2.9 Hz C) 5.7 Hz D) 4.0 Hz E) 1.7 Hz A solid sphere of mass 9.4 kg, made of metal whose density is 4400 kg/m^3, hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 43 N. The density of the liquid is closest to which one of the following values? A) 2200 kg/m^3 B) None of the Choices C) 2000 kg/m^3 D) 1900 kg/m^3 E) 2300 kg/m^3 F) 1700 kg/m^3

Explanation / Answer

k = 2E / A²
k = [(2)(4.0 J)] / [(0.20 m)²]
k = 325 kg / s²

Then:

= 2f
f = [1 / (2)] (k / m)
f = [1 / (2)] [(325 kg / s²) / (0.25 kg)]
f 5.7 Hz

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