Answer to Question #287070 in Mechanics | Relativity for Dave

Question

A system consists of a 2.0kg mass hanging from a vertical spring that has a spring constant of 8.0N/m. The system is displaced 20.0cm and continues to vibrate with no damping (meaning that there are no losses so the system oscillates forever).

a. Determine the period of oscillation.

b. Sketch a graph of two complete oscillations of the system as a

displacement-time graph.

c. On the graph, indicate where the maximum velocity and acceleration

will occur.

d. Calculate the maximum values for:

i. Spring force

ii. Acceleration of the mass

iii. Velocity of the mass

Answer 1

$a.\space T=2\pi\sqrt{m/k}=3.14\text{ s}.$

b, c.

$d.\space F_\text{max}=kx_\text{max}=1.6\text{ N}.\\ \space \space \space \space a=F_\text{max}/m=0.8\text{ m/s}^2.\\ \space \space \space \space v=x\sqrt{k/m}=0.4\text{ m/s}.$