A heavy 7 kg mass on a weak 12 N/m spring oscillates with an amplitude of 23 cm. At what frequency in Hz does the mass oscillate?
To find the frequency at which the mass oscillates, we can use the formula for the frequency of simple harmonic motion:
f = (1 / (2π)) * sqrt(k / m),
where f is the frequency, k is the spring constant, and m is the mass.
Given:
k = 12 N/m
m = 7 kg
Substituting the given values into the formula, we get:
f = (1 / (2π)) * sqrt(12 N/m / 7 kg)
Now, simplify the expression:
f = (1 / (2π)) * sqrt(12 / 7) Hz
To calculate the numerical value, substitute the approximate value for √(12/7) and evaluate:
f ≈ (1 / (2π)) * (1.2309) Hz
f ≈ 0.1969 Hz
Therefore, the mass oscillates at approximately 0.1969 Hz.