Question 196: Oscillations

Question

Time period of a simple pendulum is T. The time taken to complete $${5 \over 8}$$ oscillations starting from mean position is $${\alpha  \over \beta }T$$. The value of $$\alpha$$ is _________.

Accepted Answer

$${5 \over 8}$$ oscillation = $${1 \over 2}$$ oscillation + $${1 \over 8}$$ oscillation
From figure, A to B = $${1 \over 2}$$ oscillation and B to C is $${1 \over 8}$$ oscillation.
$$ 	herefore $$ $$\pi { + \,	heta  = \omega t} $$
$$ \Rightarrow $$ $$\pi { + {{\pi{} } \over 6}}  = \omega t$$
$$ \Rightarrow $$ $${{7\pi {} } \over 6} = \left( {{{2\pi {} } \over T}} ight)t$$
$$ \Rightarrow $$ t = $${{7T} \over {12}}$$

Oscillations

Time period of a simple pendulum is T. The time taken to complete ${5 \over 8} oscillations starting from mean position is {\alpha \over \beta }T. The value of \alpha$ is _________.

Integer / Numeric Answer Type