Three springs are connected to a block of mass 'm' having spring constant 'k' . Angle between the springs is 120 degree. Slightly displace the object from mean position and find the time period.
Answers
The time period of the object from the mean position is T= 2π √ 2m /k
Explanation:
When particle of mass m at o is pushed by x, the spring A will be compressed by x while spring B will be stretched by x' = x cos(60°)
Total restoring force on mass m
m = FA + FB cos (60°) + Fc cos (60°)
m = kx - kx'cos(60°) -kx'cos(60°)
m = - kx - 2kx'cos (60°)
m = -kx [ x + 2x cos(60°) (cos60°) ]
m = - kx [ 1 + x x 1/2 x 1/2 ]
m = - kx/2 = k'x
Where k' = k/2
T = 2π √ m / k
T = 2π √ m / k/2
T = 2π √ 2m /k
Thus the time period of the object from the mean position is T= 2π √ 2m /k
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