Question

1 A massless spring with spring constant ? hangs from the ceiling with a small object of mass ? attached to its lower end. The object is initially held at the spring’s rest position. The object is then released oscillates up and down, with its lowest position being 10 ?? below the point from which it was released. a) What is the value of the ratio of the spring constant of the spring over the mass attached? That is, what is ?/?? b) What is the frequency of the oscillation? c) What is the speed of the object when it is 8.0 ?? below the initial position? d) An object of mass 300 ? is attached to the first object, after which the system oscillates with half the original frequency. What is the mass of the first object?

Answer 1

a)Amplitude A=10cm=0.1m

mg=kA

k/m=g/A=9.8/0.1=98= (g=9.8m/s2)

==

b)frequency f=/2=/2=1.576Hz

c)speed v=

x=displacement=8cm=0.08m

v=x=0.594m/s

d)first mass =m

new mass =m+300

original frequency f=/2

New frequency f'=/2

f'=f/2

/2=/4

=/2

squaring

k/(m+300)=k/4m

m+300=4m

3m=300

m=100gram=mass of first object