In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00 kg body vibrates at 1.00 Hz, a 2.00 kg body will vibrate at
A) 0.500 Hz.
B) 0.707 Hz.
C) 1.00 Hz.
D) 1.41 Hz.
E) 2.00 Hz.

Question

Quizplus · Accepted Answer

The frequency of a simple harmonic oscillator depends on the mass and the spring constant. The formula for the frequency is given by:
f = 1/(2π)√(k/m)
where f is the frequency, k is the spring constant, and m is the mass. 
Since the spring constant and the support remain the same, we can equate the formula for the two masses:
f1 = 1/(2π)√(k/1)
f2 = 1/(2π)√(k/2)
Dividing these two equations gives:
f2/f1 = √(k/2)/√(k/1) 
f2/f1 = √2 
f2 = f1√2 
Substituting f1 = 1 Hz, we get:
f2 = 1 Hz x √2 ≈ 0.707 Hz 
Therefore, the 2.00 kg body will vibrate at approximately 0.707 Hz or choice B.

In an Inertia Balance, a Body Supported Against Gravity Executes