Homework 15 - due Friday October 11
1. In class we showed that for small amplitude oscillations the dierential
equation governing the motion of the simple pendulum is:
d2
= 2
2
dt
where =
g
L
. This D.E. has the general solution
(t) = o cos(t + )
where
Homework 23
1. Show that f = 0 for any scalar function f (x, y, z) . Because of
r
this identity, if we dene a conservative force as Fc = U(), where
l
U is the potential energy, we ensure that F = 0 and F d = 0.
2. Find the force for the following potent
PHYS 2P20: Introductory Mechanics
(Fall 2012/13)
Instructor: Kirill Samokhin (MC B200)
e-mail: kirill.samokhin@brocku.ca
Brock calendar entry:
Mechanics of particles and systems of particles by the Newtonian method;
conservation of linear momentum, angula
HW1 - due friday sept. 6
1. Mathematically the terminal velocity vt of an object of mass m and
cross-sectional area A falling in a uid under the inuence of gravity,
without considering buoyancy eects, is given by
vt =
2mg
ACd
where g is the acceleration d
HW5 - due wed. sept. 18
1. Consider a wheel (radius a ) rolling at constant speed a m/s in the
direction.
i
(a) At t=0, point P, which is on the rim of the wheel, is touching the
ground. Point P is at the origin at t=0. Determine the trajectory
(t) of po
HW3 - due wed. sept. 11
1. The position of a moving particle is given a function of time t to be
(t) = cos t + sin t
r
ib
jc
where b, c, are constants.
(a) Determine (t) and (t).
v
a
(b) Describe the shape of the trajectory.
(c) Is the speed constant? Ske
Homework 21
1. For a lightly damped oscillator < o ,show that the driving frequency for which the steady-state amplitude is one-half the steady-state
amplitude at the resonance frequency is given by o 3
2. Consider the force F = y + x + z 3 k. Determine t
Homework 18
1. Express the following numbers in the x + iy form. The rst four problems you should be able to do in your head, with the help of sketches
of the numbers on the Argand plane. For example, simply by sketching
you should be able to see that 1 i
BROCK UNIVERSITY
Brock University
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BROCK UNIVERSITY
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Final Examination, December 2007
Course: PHYS 2P20
Date of Examination: Dec. 7, 2007
Time of Examination: 14:0017:00
Number of pages: 2
Number of Students: 14
Number of Hours: 3
In
Homework 13 - due Monday October 7
1. A particle undergoes simple harmonic motion with an frequency of 10
Hz. Find the displacement x at any time t for the following initial
conditions:
dx
= 0.1m/s
t=0
x = 0.25m
dt
(a) Express your answer in the form x(t)
HW9 - due fri. sept. 27
1. If the force acting on a particle is known as a function of time F(t),
then the dierential equation is said to be separable and can be solved
by treating the derivatives like fractions and simple integration. That
is:
ma = F (t)
HW7 - due mon. sept. 23
1. Find the velocity v(t) and the position (trajectory) x(t) for a particle
of mass m which has speed vo and position xo at t = 0, subject to the
following forces where Fo and c are constants:
(a) Fx = Fo + ct
(b) Fx = Fo sin ct
2.