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[题1] 图1所示为地震仪中的无定位摆。质量M、长l的刚性均匀细杆的下端固定在支点O,顶端与质量m的小球联在一起,小珠被两个劲度系数均为k的弹簧拉住固定在两边的支架上。平衡时两弹簧呈水平且保持原长,运动时细杆与弹簧均在同一竖直平面内。设系统在平衡位置附近作微小振动。试问满足什么条件时为简谐振动,并求出振动周期。 (注:当θ很小时,cosθ≈1-θ~2/2,sinθ≈θ当|x|≤
[Item 1] Figure 1 shows the no-position pendulum in the seismograph. The lower end of the rigid uniform thin rod of mass M and length l is fixed at the fulcrum O, the top end is connected with the small ball of mass m, and the beads are pulled on the brackets fixed on both sides by two springs with the stiffness coefficient k. When the two springs are balanced, the two springs are horizontal and keep the original length. During the movement, both the thin rod and the spring are in the same vertical plane. Let the system make a slight vibration near the equilibrium position. Ask what conditions are satisfied when the simple harmonic vibration, and find the vibration cycle. (Note: When θ is small, cosθ≈1-θ~2/2, sinθ≈θ when |x|≤