To determine the frequency at which the maximum acceleration on the shaking table equals 10g, we can use the formula for simple harmonic motion:
a_max = ω^2 * A,
where: a_max is the maximum acceleration, ω is the angular frequency, A is the amplitude of the motion.
In this case, we want the maximum acceleration to equal 10g, where 1g is equal to the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the maximum acceleration, a_max, will be 10g * 9.8 m/s^2 = 98 m/s^2.
The amplitude, A, is given as 20 mm, which is equivalent to 0.02 m.
Plugging in these values into the formula, we have:
98 m/s^2 = ω^2 * 0.02 m.
Rearranging the equation, we get:
ω^2 = 98 m/s^2 / 0.02 m = 4900 s^(-2).
Taking the square root of both sides, we find:
ω = √(4900 s^(-2)) = 70 s^(-1).
The angular frequency, ω, is related to the frequency, f, through the equation:
ω = 2πf.
Substituting the value of ω, we can solve for the frequency, f:
70 s^(-1) = 2πf.
f = 70 s^(-1) / 2π ≈ 11.13 Hz.
Therefore, the frequency at which the maximum acceleration on the shaking table equals 10g is approximately 11.13 Hz.