Question

A mass m attached to a spring oscillates with a period of 2 sec. If the mass is increased by 2kg, the period increased by 1 sec. Then find the mass m
Plz reply meeee anyone plz correct this question answer plzzzz

Answer 1

I think that is answer

Answer 2

Answer: 1.6 kg

Time period of a oscillating mass m attached to a spring is given by:

$T = 2\pi \sqrt {\frac{m}{k}}$

where, T is the period, m is the mass and k is the spring constant.

T₁ = 2  s

T₂ = 2 + 1 = 3 s

m₂ = m₁ + 2

$\frac{T_1}{T_2}= \sqrt {\frac{m_1}{m_2}} \Rightarrow \frac{2}{3}= \sqrt {\frac{m}{m+2}}\\ \frac{4}{9} = \frac{m}{m+2} \\ \Rightarrow 4m + 8 = 9 m\\ \Rightarrow 5 m = 8\\ \Rightarrow m = 1.6 kg$