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Question:
Four mass–spring systems oscillate in simple harmonic motion. Rank the periods of oscillation for the mass–spring systems from largest to smallest.
m = 2 kg , k = 2 N/m
m = 2 kg , k = 4 N/m
m = 4 kg , k = 2 N/m
m = 1 kg , k = 4 N/m
Answer:
The periods of oscillation for the mass–spring systems from largest to smallest is:
m = 4 kg , k = 2 N/m (T = 8.89 s)
m = 2 kg , k = 2 N/m (T = 6.28 s)
m = 2 kg , k = 4 N/m (T = 4.44 s)
m = 1 kg , k = 4 N/m (T = 3.14 s)
Explanation:
The period of oscillation in a simple harmonic motion is defined as the following formulation:
Where:
T = period of oscillation
m = inertia mass of the oscillating body
k = spring constant
m = 2 kg , k = 2 N/m
T = 6.28 s
m = 2 kg , k = 4 N/m
T = 4.44 s
m = 4 kg , k = 2 N/m
T = 8.89 s
m = 1 kg , k = 4 N/m
T = 3.14 s
Therefore the rank the periods of oscillation for the mass–spring systems from largest to smallest is:
m = 4 kg , k = 2 N/m (T = 8.89 s)
m = 2 kg , k = 2 N/m (T = 6.28 s)
m = 2 kg , k = 4 N/m (T = 4.44 s)
m = 1 kg , k = 4 N/m (T = 3.14 s)
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