Question

Write down the equation which describes the simple harmonic motion of a 0.4 kg mass on a spring with a spring constant k = 100 N/m, that starts its motion (at t = 0 s) at its maximum positive displacement of +0.5 m.

Answer 1

The equation which describes the simple harmonic motion is
`x=0.5\cos(15.81t)`

Step-by-step explanation:

Given that,

Mass = 0.4 kg

Spring constant = 100 N/m

Maximum displacement = 0.5 m

We need to calculate the angular frequency

`\omega=\sqrt{(k)/(m)}`

`\omega=\sqrt{(100)/(0.4)}`

We need to find the equation which describes the simple harmonic motion

Using equation of simple harmonic motion

`x = A\cos\omega t`

Where, A = amplitude

`\omega` = angular frequency

Put the value of angular frequency

`x=A\cos\sqrt{(k)/(m)t}`

Put the value in the equation

`x=0.5\cos\sqrt{(100)/(0.4)t}`

`x=0.5\cos(15.81t)`

Hence, The equation which describes the simple harmonic motion is
`x=0.5\cos(15.81t)`