Question

Figure 1 shows a load of mass 35 g attached to a vertical spring X.The load is at rest in its equilibrium position.

The load is pulled vertically downwards below its equilibrium position and released.The load oscillates with simple harmonic motion (SHM) with a period of 0.68 s and amplitude A. Figure 2 shows the variation of kinetic energy of the load with its displacement from the equilibrium position during an oscillation.

Calculate, in mm, A. The load is brought to rest and then pulled vertically downwards a distanceA2 below its equilibrium position. It is released and oscillates with SHM. Spring X has negligible mass. Sketch, on Figure 2, the variation of the total energy of the mass-spring systemwith displacement.12 morkol Spring X is replaced with an elastic string Y that obeys Hooke's law. Y has negligible mass. Y has an extension of 42 mm when the load is at rest in its equilibrium position.

The load is pulled 20 mm vertically downwards below its equilibrium position.It is then released and oscillates with SHM. Show that the period of the oscillations is approximately 0.4 s. The load on Y is now pulled 50 mm vertically downwards below its equilibrium positionand released. The movement of the load fulfils the conditions for SHM until the load reaches aposition P. When the load is at P, the elastic string Y is at its unstretched length. Calculate the velocity of the load at P. The load continues to move upwards after reaching P. Explain why this movement above P does not fulfil the conditions for SHM. State whether spring X or elastic string Y has the greater stiffness.Explain your answer.

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