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Three identical 8.5 kg masses are hung by three identical springs. If the masses are displaced and released, what is the frequency of oscillation of the system?

A. 1 Hz
B. 2 Hz
C. 3 Hz
D. 4 Hz

User Nadia
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1 Answer

3 votes

Final answer:

To find the frequency of oscillation of the system, the formula f = 1 / (2π) * √(k / m) can be used. Since the three masses are identical, the total mass (m) is 3 times the mass of each individual mass. Therefore, option D in the answer choices).

Step-by-step explanation:

To find the frequency of oscillation of the system, we can use the formula:

f = 1 / (2π) * √(k / m)

Where:

  • f is the frequency
  • π is a mathematical constant approximately equal to 3.14
  • k is the spring constant
  • m is the mass

Since the three masses are identical, the total mass (m) is 3 times the mass of each individual mass. Let's assume the spring constant (k) is the same for all three springs.

Therefore, the frequency of oscillation of the system is:

f = 1 / (2π) * √(k / (3m))

Since the mass of each individual mass is 8.5 kg, we can substitute the values into the formula:

f = 1 / (2π) * √(k / (3 * 8.5 kg))

Simplifying the formula, we get:

f = 1 / (2π) * √(k / 25.5 kg)

Therefore, the frequency of oscillation of the system depends on the spring constant (k), but not on the mass (m). So, the rate of oscillation is independent of the force constant (option D in the answer choices).

User Lineil
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