Question

What is the period if the block’s mass is doubled? Note that you do not know the value of either m or k, so do not assume any particular values for them. The required analysis involves thinking about ratios. Express your answer to two significant figures and include the appropriate units. TT = nothing nothing

Answer 1

Answer:

2.8 seconds

Explanation:

First let us write out the formula relating the period(T),mass(m) and spring constant(k)

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

let assume $2\pi \frac{1}{\sqrt{k}}=constant=k$

hence w can write the formula as

$T=k\sqrt{m}$

if we vary k, we arrive at

$\frac{T_{1} }{\sqrt{m_{1}}}=\frac{T_{2} }{\sqrt{m_{2}}}=...=\frac{T_{n} }{\sqrt{m_{n}}}$

Now if the mass was doubled,

$m_{2} =2m_{1}$

we arrive at

$\frac{T_{1} }{\sqrt{m_{1}}}=\frac{T_{2} }{\sqrt{2m_{1}}}\\\frac{T_{1} }{\sqrt{m_{1}}}*{\sqrt{2m_{1}}}=T_{2} \\T_{1} *\sqrt{2}=T_{2}$

Since $T_{1} =2seconds$

$T_{2}=2*1.414\\T_{2}=2.8 seconds$