Question

Determine the frequency of small oscillations for a particle of mass m placed in an external field u(x)

Answer 1

The frequency of small oscillations for a particle of mass m in an external field can be determined using the formula
`f = sqrt(k/m)`. If the mass is replaced with a mass nine times as large, the frequency of the oscillations would be one-third of the original frequency.

The frequency of small oscillations for a particle of mass m in an external field u(x) can be determined using the formula:

`f = sqrt(k/m)`

Where:

f is the frequency of the oscillations

k is the spring constant (related to the external field)

m is the mass of the particle

To find the frequency with a mass nine times as large, we can substitute 9m into the formula:

`f' = sqrt(k/(9m))`

This simplifies to:

`f' = (1/3)sqrt(k/m)`

So, the frequency of the oscillations with a mass nine times as large is one-third of the original frequency.