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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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