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1.Quantum phenomena are often negligible in the “macroscopic” world. Show this numerically for the following cases
(a) The amplitude of the zero-point oscillation for a pendulum of length I = 1 m and mass m = 1 kg.
(b) The tunneling probability for a marble of mass m = 5 g moving at a speed of 10 cm/set against a rigid obstacle of height H = 5 cm and width w = 1 cm.
2.A simple pendulum has a length of 0.700 m and a mass of 1.20 kg. The maximum horizontal displacement of the pendulum bob from equilibrium is 3.00 cm. Calculate the quantum number n for the pendulum.
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3.A pendulum with a 1.00-g bob has a massless string 250 mm long. The period of the pendulum is 1.00 s.
(a) What is its zero-point energy? Would you expect the zero-point oscillations to be detectable?
(b) The pendulum swings with a very small amplitude such that its bob rises a maximum of 1.00 mm above its equilibrium position. What is the corresponding quantum number?
4. A pendulum of mass m=0.3 kg and length l = 1m is starting from rest at an angle A?¸(max) = 22 degrees. at the lowest point of the trajectory, it encounters a piece of clay of mass m = 0.1kg that sticks to the bob. What is the maximum angle reached by the pendulum?
5.A particle of mass m = 2.78 kg is suspended from a fixed point by a light inextensible string of length = 0.87 m. You are required to determine the relationship between the period of swing and the length of the pendulum for small angle approximation.
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