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
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
PHYS 2P20: Introductory Mechanics
(Fall 2012/13)
Instructor: Kirill Samokhin (MC B200)
e-mail: [email protected]
Brock calendar entry:
Mechanics of particles and systems of particles by the Ne
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,
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 a
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
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
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,
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Final Examination, December 2007
Course: PHYS 2P20
Date of Examination: Dec. 7, 2007
Time of Examination: 14:0017:00
Number o
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=
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 lik
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