Question

time taken by a simple pendulum to move from O to E is x sec and from E to B is 2x sec . what will be the time period of the pendulum shown in the picture ?

Answer 1

Answer:

refer this attachment

Answer 2

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Question}}}$

time taken by a simple pendulum to move from O to E is x sec and from E to B is 2x sec . what will be the time period of the pendulum shown in the picture ?

_____________________________________________

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \:firstly \: let's \: understand \: the \:question}}}$

in the question there is a simple pendulum and it is given that

• the time taken by 8 from point O to point E is x sec

• and from point E to point B is 2x sec .

• and we need to find the time period of the pendulum .

____________________________________________

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Formulas \: used}}}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{\boxed{\sf{ time \: period \: = \frac{total \: time \: taken}{no. \: of \: oscillation} }}}\end{gathered}\end{gathered} \end{gathered}$

_____________________________________________

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Solution}}}$

Given,

» Time taken to move from O to E = x sec

» Time taken to move from E to B = 2x sec

To find ,

» time period of the simple pendulum

~ Let's solve it ,

_____________________________________________

We know that

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{\boxed{\sf{ time \: period \: = \frac{total \: time \: taken}{no. \: of \: oscillation} }}}\end{gathered}\end{gathered} \end{gathered}$

So ,

• Total time taken = x + 2x (sec)

• No. of oscillation = ¼

~ Let's put the value..

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf{ time \: period \: = \dfrac{x + 2x}{ \dfrac{1}{4} } }}}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf{ time \: period \: = 4({x + 2x})}}}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf{ time \: period \: = 4x + 8x}}}\end{gathered}\end{gathered} \end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\large{ \longrightarrow{\sf{ time \: period \: = 12x\; sec}}}\end{gathered}\end{gathered} \end{gathered}$

$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Hence, \: total \: time \: period \: \: \underline{\underline{12x\; sec}}}}}$