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we will firstly notice the undamped case the differential equation under this case ismu ku ftit is just a non-homogeneous differential equation
it is the simplest case which we can consider unforced or free vibrations sense that ft 0 and undamped vibrations implies that g 0 under this case
it is the catch all force if there are some other forces which we decide we need to act on our object we lump them in now and call this good we
the subsequent force that we want to consider is damping this force may or may not be there for any specified problemdampers work to counteract any
spring fswe are going to suppose that hookes law will govern the force as the spring exerts on the object this force will all the time be present
there is a list of the forces which will act on the objectgravity fgthe force because of gravity will always act on the object of course such force
find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm ans
the sum of the diameters of two circles is 28 m and their difference of circumferences is 088m find the radii of the two circles ans 77
determine a particular solution for the subsequent differential equationyprimeprime - 4 yprime -12 y 3e5t sin2t te4tsolutionthis example is the
here lets take a look at sums of the fundamental components andor products of the fundamental components to do this well require the following
example find out a particular solution toy - 4y - 12 y 3e5tsolutionthe point here is to get a particular solution though the first thing that were
in this section we will see the first method which can be used to find an exact solution to a nonhomogeneous differential equationyprimeprime p t
assume that y1t and y2t are two solutions to 1 and y1t and y2t are a fundamental set of solutions to the associated homogeneous differential equation
lets here start thinking regarding that how to solve nonhomogeneous differential equations a second order linear non-homogeneous differential
1 construct an isosceles triangle whose base is 7cm and altitude 4cm and then construct another similar triangle whose sides are 12 times the
1 draw a pair of tangents to a circle of radius 2cm that are inclined to each other at an angle of 9002 construct a tangent to a circle of
draw a line segment ab of length 44cm taking a as centre draw a circle of radius 2cm and taking b as centre draw another circle of radius 22cm
find out if the following sets of functions are linearly dependent or independent a f x 9 cos 2x g x
in the earlier section we introduced the wronskian to assist us find out whether two solutions were a fundamental set of solutions under this section
determine the general solution to2t2y ty - 3y 0it given that y t t -1 is a solution solutionreduction of order needs that a solution already be
were here going to take a brief detour and notice solutions to non-constant coefficient second order differential equations of the formp t
if pa and pb are tangents to a circle from an outside point p such that pa10cm and angapb60o find the length of chord
solve the subsequent ivpy - 4y 9y 0 y0 0 y0 -8solutionthe characteristic equation for such differential equation is as r2 - 4r 9 0 the
solve the subsequent ivpyprimeprime 11yprime 24 y 0y 0 0 yprime 0-7 solutionthe characteristic equation is asr2 11r 24 0 r 8 r 3
now we start solving constant linear coefficient and second order differential and homogeneous equations thus lets recap how we do this from the