It has recently become possible to "weigh" DNA molecules with measuring the influence of their mass on a nano-oscillator. Figure shows a thin rectangular cantilever etched out of silicon density 2300 \rm kg/m^3 with a small gold dot at the end. If pulled down and released, the end of the cantilever vibrates by simple harmonic motion, moving up and down like a diving board after a jump. When bathed by DNA molecules whose ends have been modified to bind with gold, one or more molecules might attach to the gold dot. The addition of their mass causes a very slight-but measurable-decrease in the oscillation frequency. A vibrating cantilever of mass M can remodelled as a block of mass \textstyle1 \over 3\,M attached to a spring. (The factor of \textstyle1 \over 3 arises from the moment of inertia of a bar pivoted at one end.) Neither the mass nor the spring constant can be decided very accurately-perhaps to only two important figures-but the oscillation frequency can be measured by very high precision simply by counting the oscillations. In one experiment, the cantilever was initially vibrating at exactly 14 \rm MHz. Attachment of a DNA molecule caused the frequency to decrease by 53 \rm Hz. What was the mass of the DNA Textbook Solutions?