Disregading gravity, find the period of oscillation of the partical connected with four springs as shown in the figure.
`(given : theta = 45^(@). Beta = 30^(@))`

Answer

`pi sqrt((2 m)/(k))`

Explanation

`2 k sin^(2) theta = k_(1)`
or `k_(1) = 2k sin ^(2) theta`
and `k_(2) = 2 (2k) sin ^(2) beta`

Then, `k_(eq) = k_(1) + k_(2) = 2k [sin^(2) theta + 2 sin^(2) beta]`
`= 2k [ sin^(2) 45^(@) + 2 sin^(2) 30^(@) ] = 2 k ((1)/(2) +(1)/(2)) = 2k`
Then `T = 2 pi sqrt((m)/(k_(eq))) = 2 pi sqrt ((m)/(2k)) = pi sqrt((2 m)/(k))`