A small trolley of mass 2 kg resting on a horizontal frictionless turntable is connected by a light spring to the centre of the table. The relaxed length of the spring is 35 cm. When the turntable is rotated an angular frequency of 10 rad s–1, the length of the spring becomes 40 cm. what is the force constant of the spring?
The radius of the circle along which the trolley moves is
r = 40 cm = 0.4 m
When the table is rotated, the tension in the spring is equal to the centripetal force, i.e.
The extension in the spring is x = 40 – 35 = 5 cm = 0.05 m
The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as
The magnitude of the maximum acceleration of the particle is
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A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take g = 10 ms–2.
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