Although California is known for earthquakes, it has large regions dotted with p

Question

Although California is known for earthquakes, it has large regions dotted with precariously balanced rocks that would be easily toppled by even a mild earthquake. The rocks have stood this way for thousands of years, suggesting that major earthquakes have not occurred in those regions during that time. If an earthquake were to put such a rock into sinusoidal oscillation (parallel to the ground) with a frequency of 2.10 Hz, an oscillation amplitude of 1.40 cm would cause the rock to topple.What would be the magnitude of the maximum acceleration of the oscillation, in terms of g?

Explanation / Answer

Given: Xmax=1.4 cm = .014 m f= 2.10 Hz g=9.8 First you need to solve for T ( the period) = 1/frequency. T= 1/f T= 1/2.10 Hz T= 0.47619 From there, plug that into the equation of the magnitude of maximum acceleration. A= ( (((2*pi) / T)^2) * Xmax ) / g A= ( (((2*pi) / 0.47619) ^2) * 0.014 m ) / 9.8 A= 0.2487

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