a mass is suspended from two coupled springs connected in series. the force constants for springs are k1 & k2. What is the time period of suspended mass???
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F = -k1 x y 1
F= - k2 x y2
y = y1 x y2
= y1 + y2
= -( F / k1) - (F / k2)
= - F [ (1/ k1 ) + ( 1/ k2) ]
= -F [ k2 + k 1 / k1 x k2 ]
F = - ( k1 x k2 / k1 + k2 )
F = - ky
K = k1 x k2/ k1 + k2
T = 2 pi under root m/ k
T = 2 pi under root m ( k1 + k2 ) / k1 x k2
k1 = k2 = k
K = k / 2
T = 2pi root 2m / k
F= - k2 x y2
y = y1 x y2
= y1 + y2
= -( F / k1) - (F / k2)
= - F [ (1/ k1 ) + ( 1/ k2) ]
= -F [ k2 + k 1 / k1 x k2 ]
F = - ( k1 x k2 / k1 + k2 )
F = - ky
K = k1 x k2/ k1 + k2
T = 2 pi under root m/ k
T = 2 pi under root m ( k1 + k2 ) / k1 x k2
k1 = k2 = k
K = k / 2
T = 2pi root 2m / k
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