Question

A weight of 35.0 N is suspended from a spring that has a force constant of 220 N/m. The system is undamped and is subjected to a harmonic driving force of frequency 10.5 Hz, resulting in a forced-motion amplitude of 3.00 cm. Determine the maximum value of the driving force.

Answer 1

The force is
`F = 423.04 \ N`

Step-by-step explanation:

From the question we are told that

The weight is
`W = 35 .0 \ N`

The force constant is
`k = 220 \ N/m`

The frequency is
`f = 10.5 \ Hz`

The amplitude is
`A = 3.00 \ cm = 0.03 \ m`

Generally the maximum driving force is mathematically represented as

`F = m * w^2 A`

Here m is the mass of the weight which is mathematically represented as

`m = ( W )/(g)`

=>
`m = ( 35 )/(9.8 )`

=>
`m = 3.571 \ kg`

Also
`w` is the angular frequency of the weight which is mathematically represented as

`w = 2 \pi * f`

`w = 2* 3.142 * 10`

=>
`w = 62.84 \ rad/s`

So

`F = 3.571 * 62.84^2 * 0.03`

`F = 423.04 \ N`