What is the maximum acceleration of a platform that oscillates with an amplitude of 3.1 cm at a frequency of 8.0 Hz?
To find the maximum acceleration of a platform oscillating with a given amplitude and frequency, we can use the formula for acceleration in simple harmonic motion.
The formula for acceleration in simple harmonic motion is:
a_max = ω^2 * A
where:
a_max is the maximum acceleration
ω (omega) is the angular frequency (2πf) in radians per second
A is the amplitude of the oscillation
First, we need to find the angular frequency ω. The angular frequency is calculated by multiplying 2π (pi) by the frequency (f) in hertz. In this case, the frequency is given as 8.0 Hz. So:
ω = 2π * f
= 2π * 8.0 Hz
Next, we can substitute the values of ω and A into the formula:
a_max = (2π * 8.0 Hz)^2 * 3.1 cm
Finally, we can calculate the maximum acceleration:
a_max = (2π * 8.0)^2 * 3.1 cm
To obtain the answer, simply evaluate the expression using a calculator.