Below is shown the graph of the x position of an oscillating system measured by

Question

Below is shown the graph of the x position of an oscillating system measured by a sonic ranger but the origin is shifted so that the 0 of the coordinate occurs at the equilibrium point of the system.

A. Assume that the graph represents the position of a wooden disk hanging on a spring from a bar and that x is the up-down coordinate with + being up. (The loose spring next to the hanging disk is identical to the one the disk is hanging from.)

A1. The mass of the disk is 500 g. Find the spring constant, k.

k=_____ N/m

A2. How much will the spring be stretched when the mass is at the equilibrium point?

?L =_____ m

Explanation / Answer

5 cm is the maximum extension in spring.... i.e amplitude of the graph

so at this point, the energy is completely in the spring.= 1/2*K*(x)^2

at the top extreme point i.e 5 cm above equilibrium, energy = m*g*H = 500*9.8*10*10^-2 = 490J

so 1/2*K*(x)^2 = 490J

1/2*K*0.05^2 = 490

K = 39200 N/m

also at equilibrim, forces are to be balanced.... so mg = kL

500*9.8 = k*L = 39200 L

so L = 0.125 m = 12.5 cm

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