Answer:
New time period, [tex]T_2=2.12\ s[/tex]
Explanation:
Given that,
Mass of the object 1, [tex]m_1=0.75\ kg[/tex]
Time period, [tex]T_1=1.5\ s[/tex]
If object 1 is replaced by object 2, [tex]m_2=1.5\ kg[/tex]
Let [tex]T_2[/tex] is the new period of oscillation.
The time period of oscillation of mass 1 is given by :
[tex]T_1=2\pi \sqrt{\dfrac{m_1}{k}}[/tex]
[tex]1.5=2\pi \sqrt{\dfrac{0.75}{k}}[/tex]............(1)
The time period of oscillation of mass 2 is given by :
[tex]T_2=2\pi \sqrt{\dfrac{m_2}{k}}[/tex]
[tex]T_2=2\pi \sqrt{\dfrac{1.5}{k}}[/tex]............(2)
From equation (1) and (2) we get :
[tex](\dfrac{T_1}{T_2})^2=\dfrac{m_1}{m_2}[/tex]
[tex](\dfrac{1.5}{T_2})^2=\dfrac{0.75}{1.5}[/tex]
[tex]\dfrac{1.5}{T_2}=0.707[/tex]
[tex]T_2=2.12\ s[/tex]
So, the new period of oscillation is 2.12 seconds. Hence, this is the required solution.
