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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
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
```