prob2 - APSC 112 Problem Set 2 Rigid Body Oscillations The...

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Unformatted text preview: APSC 112 Problem Set 2 Rigid Body Oscillations . The thin square plate shown in Fig. 1 has side a = 20cm and a hole of radius 5cm at its centre. The mass of the plate is 1.5kg. It has one side attached to a smooth horizontal axle, and hangs vertically. (a) What is the moment of inertia of the plate about the axle? (b) What is the period of small oscillations about the equilibrium position? The moment of inertia of a disc of radius R about an axis which lies along a diameter is MRZM. . A small hole is bored in a metre rule a distance x from the 50cm mark, as shown in Fig. 2. The rule is suspended from a horizontal nail in the hole, and oscillates as a pendulum. What should it be if the frequency of oscillation is to be a minimum? See Fig. 3. A thin square plate of mass 0.50kg and side 30cm is attached to the middle of a thin rod of length 80cm and mass 0.25kg. The rod hangs vertically, and can freely rotate about either a pivot at its centre or a pivot P at its top. Two springs of force constant k] = 10 me and k2 = 15 me are attached to the bottom as shown. (a) Show that the two springs are equivalent to a single spring with k = 6 N/m. (1:) Determine the period of small oscillations about the equilibrium position when the system is pivoted (i) at its centre, or (ii) at P. The thin rod of length L and mass m has one end freely pivoted at P, and the other end attached to a spring of force constant k. In the equilibrium position, the rod is horizontal. (a) By how much is the spring compressed at equilibrium? (b) If the end of the rod in contact with the spring is pushed down slightly and released, what is the frequency of the resulting oscillation? . A thin rod of length L = 1.0m and mass M = 0.6kg is freely pivoted at one end, as shown in Fig. 5. To the lower end of the rod are attached two strings which pass over two light pulleys and support two equal masses m = 0.1kg. If one of the masses is pulled down a short distance, what is the period of the resulting oscillations? ...
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