Question

A very light spring is 10.0 cm long with no mass attached to it. When 50.0 g are added, its length increases to 11.25 cm. Another 100 g is added and it sets into oscillation. How much time is needed for 100 oscillations.

Answer 1

38.847 seconds

Step-by-step explanation:

m = Mass

x = Compression of spring

k = Spring Constant

g = Acceleration due to gravity = 9.81 m/s²

`F=mg`

From Hooke's law

`F=kx\\\Rightarrow 0.05* 9.81=k(11.25-10)* 10^(-2)\\\Rightarrow k=(0.05* 9.81)/((11.25-10)* 10^(-2))\\\Rightarrow k=39.24\ N/m`

Additional mass

m = 0.1+0.05 = 0.15 kg

Angular frequency

`\omega=\sqrt{(K)/(m)}\\\Rightarrow \omega=\sqrt{(39.24)/(0.15)}\\\Rightarrow \omega=16.17405\ rad/s`

Time for one oscillation is given by

`T=(2\pi)/(\omega)\\\Rightarrow T=(2\pi)/(16.17405)\\\Rightarrow T=0.38847`

For 100 oscillations

`100* 0.38847=38.847\ s`

The time needed for hundred oscillations is 38.847 seconds