To find the threshold angular frequency (w) at which the small drawer on the floor starts to create periodic thuds, we can make use of the relationship between angular frequency, amplitude, and acceleration in simple harmonic motion.
In simple harmonic motion, the acceleration (a) of an object is directly proportional to the angular frequency (w) and the displacement (x) from the equilibrium position. The relationship can be expressed as follows:
a = -w^2 * x
Where:
- a represents the acceleration
- w represents the angular frequency
- x represents the displacement (amplitude in this case)
Given that the amplitude (x) is 2 cm, we can substitute the values into the equation:
a = -w^2 * 0.02
Now, the "thuds" occur when the acceleration reaches a certain threshold value. Let's assume that this threshold acceleration is represented by a threshold value (a_th).
So, we can set up the equation as:
a_th = -w^2 * 0.02
To find the threshold angular frequency (w), we rearrange the equation:
w^2 = -a_th / 0.02
Taking the square root of both sides:
w = sqrt(-a_th / 0.02)
The negative sign indicates that the acceleration is in the opposite direction of the displacement.
Therefore, by knowing the threshold acceleration value (a_th), you can calculate the threshold angular frequency (w) using the above equation.