What is the maximum acceleration of a platform that oscillates with an amplitude of 2.1 cm at a frequency of 6.7 Hz?
I feel like this is a very simple question, but I'm having trouble figuring it out.
To find the maximum acceleration of a platform oscillating with a given amplitude and frequency, you can use the formula for simple harmonic motion:
a_max = (2πf)^2 * A
Where:
- a_max is the maximum acceleration
- f is the frequency of oscillation in Hz
- A is the amplitude of the oscillation in meters
In this case, the given amplitude is 2.1 cm, which can be converted to meters by dividing by 100:
A = 2.1 cm / 100 = 0.021 m
The given frequency is 6.7 Hz. Plugging these values into the formula:
a_max = (2π * 6.7)^2 * 0.021
Now we can simplify the calculation by using approximate values for π:
a_max ≈ (6.28 * 6.7)^2 * 0.021
Performing the calculation:
a_max ≈ 2.097 * 0.021
a_max ≈ 0.044 m/s^2
Therefore, the maximum acceleration of the platform is approximately 0.044 m/s^2.