This is a practice problemanswer is Better with explanationsThank you! Excuse th

Question

This is a practice problemanswer is Better with explanationsThank you!

Excuse the image, I can't work that out......

1-RI rul L SCREEN PREMIER VERSaur, 'BACK Chapter 15, Problem 037 A massless spring hangs from the ceiling with a small cbject attached to ts lower end. The object is initally held at rest in a position w such that the spring is at its rest kength. The object is then relessed from y, and osollates up and down, with ts lowest position being 11 cm below y (a) What is the frequency of the oscilation? (b) What is the speed of the object when it is 9,7 cm below the nitial position? (c)An object of mass 300 g is attached to the first object, after which the system asallates with half the original frequency. Whst is the mass of the first obgect? (d) How far below y, is the new equlibrium (rest) position with both objects attached to the sping? (a) Number (b) Number (c) Number (d) Number Unts ursts Unsts SHOW HINT PROBLEN TO SAMPLE By accessing thes Question Assistanoe, you swill learn while you earn points based on the Point Potentisal Poicy set by your instructot. Question Altemgpts: 0 of S used SAME FOR LATER SUDMEIT ANESWCER rn Maximum Peints available only you

Explanation / Answer

We have to assume that "at its rest length" means "at its UNLOADED rest length"; otherwise, it would not need to be held. Then twice the amplitude = 11cm, and A = 5.5cm
F = kx
m·9.8m/s² = 0.055m·k
k/m = 9.8/0.055s² = 178.2 /s²
sqrt(k/m) = 13.35/s
f = 13.35/2s = 2.12/s (a)

b) max Ep = ½k·(0.055m)² = 1.5e-3m²·k
at y = 9.7cm, Ep = ½k(0.015m)² = 1.1e-4m²·k
E = 1.4e-3m²·k
This must have become kinetic energy, Ek = ½mv²
Set them equal, and solve for v²:
v² = 1.4e-3m²·2·k/m
From above, we have k/m = 178.2 /s²
v = sqrt(1.4e-3m² · 2 · 178.2/s²) = 0.71 m/s


c) sqrt(k/(m + 0.3kg) )= ½sqrt(k/m)
square both sides
k/(m+0.3kg) = k/(4m)
m + 0.3kg = 4m
3m = 0.3kg
m = 0.1kg = 100 gm


d) we've quadrupled the force on the spring; therefore we've quadrupled the displacement.
4 *5.5cm = 22cm

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