# A block of unknown mass is attached to a spring with a spring constant of 10 N/m and undergoes simple harmonic motion with an amplitude of 8.0 cm. When the block is 1/4 of the way between its...

A block of unknown mass is attached to a spring with a spring constant of 10 N/m and undergoes simple harmonic motion with an amplitude of 8.0 cm. When the block is 1/4 of the way between its equilibrium position and the endpoint, its speed is measured to be 30.0 cm/s. Calculate the mass of the block and period.

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To solve this problem, the knowledge of the Hooke’s law is necessary.

Given:

Spring constant (k) = 10 N/m

amplitude = x(max) = 8.0 cm = 0.08 m

speed (v) = 30.0cm/s 0.3 m/s

1. Calculate the mass of the block

`omega = (v)/(x_(max)) = sqrt(k/m)`

`omega = (0.3)/(0.08) = sqrt(10/m)`

`omega = 3.75 = sqrt(10/m)`

`(3.75 = sqrt(10/m))^(2)`

`3.75^(2) = 10/m`

`m = 10/(3.75^(2))`

`m = 0.71 kg`

2. Calculate the period, T

`omega = (2 pi)/T`

`3.75 = (2 pi)/T`

`T = (2 pi)/3.75`

`T = 1.68 s`