F = k * a = μ * mg, a is the amplitude, k is the recovery coefficient, and m is the mass of the object.
Get k/m = μ g/a.
Because the period of simple harmonic motion is t = 2π * root sign (m/K).
The frequency is f = 1/t =[ root sign (K/m)]/(2π).
That is, 2 =[ radical sign (μ g/A)]/(2π)
2 =[ root number (0.5 *10/a)]/(2 * 3.14)
The maximum amplitude sought is a = 0.032m = 3.2cm.
(2) If this plate is simple harmonic motion in the vertical direction, the acceleration of the highest point (maximum displacement) is equal to the acceleration of gravity g..
At this time, k 1 * A 1 = mg, k 1 is the recovery coefficient, and A 1 is the amplitude.
K 1 / m=g / A 1
As with the above question, there is a frequency f 1 =[ root sign (K 1/m)]/(2π).
That is, the maximum frequency is f 1 =[ root number (g/A 1)]/(2π).
= [root number (10/0.05)]/(2 * 3.14)
=2.25 Hz