Question

A mass of 0. 40 kg, hanging from a spring with a spring constant of 160 n/m, is set into an up-and-down simple harmonic motion. What is the speed of the mass when moving through the equilibrium point? the starting displacement from equilibrium is 0. 10 m.

Answer 1

Given:

`m=0.40kg`

`k=160(N)/(m)`

`A=0.10m`

We know that the velocity of a mass attached to a spring is greatest when passing through equilibrium. Using the following formulas we can compute velocity.

`v_(max) =\pm Aw` and
`w=\sqrt{(k)/(m) }`
`\Longrightarrow v_(max) =\pm A\sqrt{(k)/(m) }`

`\Longrightarrow v_(max) =\pm A\sqrt{(k)/(m) }`

`\Longrightarrow v_(max) =\pm (0.10)\sqrt{(160)/(0.40) }`

`\Longrightarrow v_(max) =\pm (0.10)(20) }`

`\Longrightarrow v_(max) =\pm 2.0(m)/(s)`