cameroon gce A level June 2024 further mathematics 3
cameroon gce A level June 2024 further mathematics 3
A particle /’moves in a resistive medium such that its displacement,.’/.’,
from a fixed point ( ) satisfies the differential equation
undergoes damped harmonic
marks)
h) A particle / moves on a curve with constant angular velocity to. Its radial and
transveise components of acceleration at time / seconds are given by
(itv^(4 (’.os0 — 1) and 4a///2 sin0 respectively.
Find the magnitude of the acceleration of P and deduce that its maximum value
is !)(iu )2 m.s ~2 .
(It
motion, find the period and the damping factor. (5 r/tfrk S.
(5 marks)
5. a) A particle /?, moves on the curve C whose polar coordinates arc (‘/ *,/?), with constant
angular velocity w . Given that the radial and transverse components of the acceleration
of P are
— 2a?//2(l+ cos 0 ) and —2a?//2 sin0 respectively,
where a is a constant, show that the equation of the curve C is r = a(2 + cos0). (6 marks)
b) A particle is executing simple harmonic motion between two points A and B which
are 5m apart. The maximum velocity of the particle is 5m’ .s-1.
Find
i) the period ofmotion of the particle.
ii) the maximum acceleration.
(3 marks)
(2 marks)
6. A uniform rod AB of mass 3m and length’4a has a particle of mass 2m attached to the end B.
i) Show that the moment of inertia of the system about an axis through A which is
perpendicular to the plane of the rod is 48?/m2.
ii) Find the distance, from A,of the centroid of the system.
The rod is smoothly hinged about a horizontal axis through A and then released from rest.
iii) Show that when the rod makes an angle 0 with the horizontal,
12^afd—# )2 = 7^/7 suit • /,/ .
(3 marks)
(2 marks)
(5 marks)
dl.
7. A particle of unit mass falls vertically from rest in a resistive medium, where the resistance is
proportional to the speed’if , of the particle. When the particle is moving with speedu,
the resistive force is equal to half the force of gravity (g) on the particle.
A
Show that at time /,
do
, v
i) v — = (/ 1 .
dx 2u
(6 marks)
ii) the particle has covered a distance x —^
