Question

A block of mass m is attached atthe end of a spring of force constant 10N/m vibrates in SHM with frequency of 10/bi Hz. Find the mass of the block

Answer 1

The mass of the block is 0.025 kg

Step-by-step explanation:

Mass-Spring Harmonic Motion

When a mass m is attached to a spring of constant k, they produce a simple harmonic motion which angular frequency is

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

We also know

`w=2\pi f`

which means

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

Squaring

`\displaystyle (k)/(m)=4\pi^2 f^2`

Solving for m

`\displaystyle m=(k)/(4\pi^2 f^2)`

We have

`k=10 N/m, f=10/\pi Hz`

`\displaystyle m=(10)/(4\pi^2 \left ((10)/(\pi)\right )^2)`

Operating

`\displaystyle m=(10)/(4\pi^2 (100)/(\pi^2))`

Simplifying and computing

`\displaystyle m=(1)/(40)=0.025\ kg`

The mass of the block is 0.025 kg