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bug running on a hoop a uniform circular hoop of mass m can slide freely on a smooth horizontal table and a bug of mass
in the theory of dynamical systems a point is said to be an asymptotically stable equilibrium point if it lsquoattracts
projectile using cartesian coordinates find the hamiltonian for a projectile of mass m moving under uniform gravity
a smooth wire has the form of the helix x a cos theta y a sin theta z btheta where theta is a real parameter and a b
a particle is constrained to move over a smooth fixed surface under no forces other than the force of constraint by
a heavy uniform rope of length 2a is draped symmetrically over a thin smooth horizontal peg the rope is then disturbed
a uniform heavy rope of length a is held at rest with its two ends close together and the rope hanging symmetrically
a heavy uniform rope of mass m and length 4a has one end connected to a fixed point on a smooth horizontal table by
consider the system shown in figure 912 for the special case in which the particles p q have masses 2m m respectively
given figure shows two blocks of masses m and m that slide on smooth planes inclined at angles alpha and beta to the
the internal gravitational potential energy of a system of masses is sometimes called the self energy of the system the
a uniform rod of length 2a has one end smoothly pivoted at a fixed point o the other end is connected to a fixed point
van der pols equation use poincare-bendixson to show that van der pols equationxmiddotmiddot isinxmiddotx2-1 x 0has
a driven non-linear oscillator satisfies the equationxmiddotmiddot isinxmiddot3 x cos ptwhere p are positive
linstedts method use computer assistance to implement lindstedts method for the equationxmiddotmiddotxisinx30obtain a
a uniform ball is rolling in a straight line down a rough plane inclined at an angle alpha to the horizontalassuming
a uniform circular cylinder a yo-yo has a light inextensible string wrapped around it so that it does not slip the free
a rigid body of general shape has mass m and can rotate freely about a fixed horizontal axis the centre of mass of the
a uniform ball of radius a can roll without slipping on the outside surface of a fixed sphere of outer radius b and
a uniform ball of radius a and centre g can roll without slipping on the inside surface of a fixed hollow sphere of
show that if a system moves from one state of rest to another over a certain time interval then the average of the
show that if a system moves periodically then the average of the total external force over a period of the motion must
a boat of mass m is at rest in still water and a man of mass m is sitting at the bow the man stands up walks to the
a fine uniform chain of mass m and length a is held at rest hanging vertically downwards with its lower end just
a uniform ball of mass m and radius a can roll without slipping on the rough outer surface of a fixed sphere of radius