An object of mass m is hung from a spring and set into oscillation. The period of the oscillation is measured and recorded as T. The object of mass m is removed and replaced with an object of mass 2m. When this object is set into oscillation, what is the period of the motion?

When the mass is replaced by 2m . Then,  time period become times of previous time period.

Let us consider that , an object of mass m is attached to spring and set into oscillation.

Time period is defined as, number of oscillation per second.

Period of oscillation,  

Wen mass is replaced by 2m. then period of oscillation is T' .

Therefore, When the mass is replaced by 2m . Then period become times of previous time period.

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Explanation:

Given

object of mass m is suspended from spring and set in oscillation with time Period T

We know Time period of a mass in oscillation is given by

where k=spring constant

When mass m is replaced by a mass of 2 m time period is given by

i.e. New time period becomes times of previous one

the area between the graph and the t axis

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day