Question

Using the mks units (meters-kilograms-seconds), suppose you have a spring with spring constant 4 N/m. You want to use it to weigh items. Assume no friction. You place the mass on the spring and put it in motion. a) You count and find that the frequency is 0.8 Hz (cycles per second). What is the mass? b) Find a formula for the mass m given the frequency ω in Hz

Answer 1

Our values,

`f= 0.8Hz`

`k= 4N/m`

We can find the angular velocity,

`w=2\pi f`

`w=2\pi(0.8)`

`w=5.02rad/s`

a) To calculate the mass we know that the formula of

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

Re-arrange for the mass

`m=(k)/(w^2)=(4)/(5.02^2) = 0.15872Kg`

b) We can use the latest equation to make a relation between the mass and the frquency,

We have that,

`w=2\pi f` (1)

`w=\sqrt{(k)/(m)}` (2)

Making equal ,

`2\pi f=\sqrt{(k)/(m)}`

Re-arrange to m,

`m = (k)/((2\pi f)^2)`