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 * radical sign (m
/
k)
The frequency is F.
= 1
/
T =[ root symbol (k
/
m)]
/
(2π)
That is 2 =[ root 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 the plate is in a simple harmonic vibration in the vertical direction, the acceleration at the highest position (the maximum displacement position) 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
Like the above question, there is a frequency f 1 =[ root sign (k 1
/
m)]
/
(2π)
That is, the maximum frequency is f 1 =[ root symbol (g
/
a 1)]
/
(2π)
= [Root symbol (10
/
0.05)]
/
(2*3. 14)
=2.25
hertz