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COLLEGE OF SCIENCE AND TECHNOLOGY P.O. Box 3900 Kigali, Rwanda DEPARTMENT OF PHYSICS Course: PHYSICS FOR ENGINEERS I (PHY1163) 1st Year MINING & GEOLOGY (2020/21) Lecturer: Dr. Christian KWISANGA ASSIGNMENT 5: SIMPLE HARMONIC MOTION (40 Marks) 1. A solid cylinder is attached to a horizontal spring rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250m. Find the translational kinetic energy and the rotational kinetic energy of the cylinder as it passes the equilibrium position. Find the resonance frequency of the system from energy conservation equations (Fig.1a). (Hint: use the energy conservation theorem) (a) Q1 (c) Q2 (b) Q3 Figure 1. Graphs for questions 1-3 2. A grandfather’s clock has a pendulum (Fig.1c) that consists of a thin disk of brass of radius cm and a mass of Kg that is attached along a thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite to the disk. If the pendulum is to have a period of 2s for small oscillations at a place where m/s2. What is the rod length to achieve that? (Hint: use the conservation of linear momentum theorem) 3. A solid sphere (radius R) rolls without slipping in a cylindrical trough (radius 5R) as shown in Fig.1b. find the resonance frequency of the sphere, for small displacements from equilibrium perpendicular to the length of the trough. (Hint: use the conservation of energy theorem). 4. A body in a shape of the letter C (the gap f=60o) is dangling upside down on an axle as shown in Fig.2a. Find the resonance frequency of the motion given that the angles are small. (Hint: Use polar (not cartesian) coordinates) 5. A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (Fig. 2b). Find the frequency of resonance of the system for small values of the amplitude (small ). Assume the vertical suspension of length L is rigid but ignore its mass. (Hint: Picture all the forces acting on mass M and use the 2nd law on Newton). axle a b (a) Q4 (b) Q5 Figure 2. Graphs for questions 4-5