Four mass–spring systems oscillate in simple harmonic motion. Rank the periods of oscillation for the mass–spring systems from largest to smallest.

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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.

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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:

  1. m = 4 kg , k = 2 N/m (T = 8.89 s)
  2. m = 2 kg , k = 2 N/m (T = 6.28 s)
  3. m = 2 kg , k = 4 N/m (T = 4.44 s)
  4. 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:

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%20%7D

Where:

T = period of oscillation

m = inertia mass of the oscillating body

k = spring constant

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m = 2 kg , k = 2 N/m

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B2%7D%7B2%7D%20%7D

?f=T%3D2%5Cpi

T = 6.28 s

m = 2 kg , k = 4 N/m

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B2%7D%7B4%7D%20%7D

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%20%7D

T = 4.44 s

m = 4 kg , k = 2 N/m

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B4%7D%7B2%7D%20%7D

?f=T%3D2%5Cpi%20%5Csqrt%7B2%20%7D

T = 8.89 s

m = 1 kg , k = 4 N/m

?f=T%3D2%5Cpi%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%20%7D

?f=T%3D%5Cpi

T = 3.14 s

Therefore the rank the periods of oscillation for the mass–spring systems from largest to smallest is:

  1. m = 4 kg , k = 2 N/m (T = 8.89 s)
  2. m = 2 kg , k = 2 N/m (T = 6.28 s)
  3. m = 2 kg , k = 4 N/m (T = 4.44 s)
  4. m = 1 kg , k = 4 N/m (T = 3.14 s)

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