# 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.

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

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: 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:

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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