Question

A 45.0 g hard-boiled egg moves on the end of a spring with force constant 25.0 N/m. Its initial displacement 0.500 m. A damping force Fx= −bvx acts on the egg, and the amplitude of the motion decreases to 0.100 m in a time of 5.00 s. Calculate the magnitude of the damping constant b. Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures.

Answer 1

0.02896 kg/s

Step-by-step explanation:

`A_1` = Initial displacement = 0.5 m

`A21` = Final displacement = 0.1 m

t = Time taken = 0.5 s

m = Mass of object = 45 g

Displacement is given by

`x=Ae^{-(b)/(2m)t}cos(\omega t+\phi)`

At maximum displacement

`cos(\omega t+\phi)=1`

`\\\Rightarrow A_2=A_1e^{-(b)/(2m)t}\\\Rightarrow (A_1)/(A_2)=e^{(b)/(2m)t}\\\Rightarrow ln(A_1)/(A_2)=(b)/(2m)t\\\Rightarrow b=(2m)/(t)* ln(A_1)/(A_2)\\\Rightarrow b=(2* 0.045)/(5)* ln(0.5)/(0.1)\\\Rightarrow b=0.02896\ kg/s`

The magnitude of the damping coefficient is 0.02896 kg/s