Respuesta :
Answer:[tex]\sqrt{2}T[/tex]
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
[tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
where k=spring constant
When mass m is replaced by a mass of 2 m time period is given by
[tex]T'=2\pi \sqrt{\frac{2m}{k}}[/tex]
[tex]T'=\sqrt{2}\times 2\pi \sqrt{\frac{m}{k}}[/tex]
[tex]T'=\sqrt{2}T[/tex]
i.e. New time period becomes [tex]\sqrt{2}[/tex] times of previous one
When the mass is replaced by 2m . Then, time period become [tex]\sqrt{2}[/tex] 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, [tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
Wen mass is replaced by 2m. then period of oscillation is T' .
[tex]T'=2\pi \sqrt{\frac{2m}{k} }=\sqrt{2}(2\pi \sqrt{\frac{m}{k} }) =\sqrt{2}T[/tex]
Therefore, When the mass is replaced by 2m . Then period become [tex]\sqrt{2}[/tex] times of previous time period.
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