An object of unknown mass oscillates on the end of a spring wit period 8 s. A 10kg object is attached to the first object, changing te period to 12 s. What is the mass of the first object

Explanation:

Let the first object have a mass of M

And a period of T1=8sec

The second object has a mass 10kg and a period of T2=12 sec

It is know that,

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

T=2π√(m/k)

Then the constant in this equation is the spring constant (k) and 2π, which does not change for the same material.

Then, make k subject of formulas

T²=4π²(m/k)

T²k=4π²m

Then, k/4π²=m/T²

So the k is directly proportional to m and inversely proportional to T²

M1/T1²=M2/T2²

Since, M1 is unknown, M2=10kg, T1=8sec and T2=12

Then,

M1/T1²=M2/T2²

M1/8²=10/12²

M1/64=0.06944

M1=0.06944×64

M1=4.444kg

The mass of the first object is 4.44kg

b) returns freshwater to the earth.

c) returns freshwater to the earth.c) occurs after condensation.

d) returns freshwater to the earth.c) occurs after condensation.d) roughly equal to the amount of evaporation.

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