School of Mechanical Engineering
Advanced Mechanics 2015
Classical Mechanics
Q1: A harmonic oscillator consists of a mass ‘m’ suspended from a spring of stiffness
‘k’ and length ‘l’. Determine the equation of motion. What is the name for this
motion?
Q2: A simple cantilever of second moment of area ‘I’ and length ‘l’ is subject to
instantaneous force ‘F’, what is the equation of motion?
Q3: For the pendulum of length ‘L’ shown in Fig3, where the block is of mass ‘M’ and
the pendulum bob mass ‘m’, determine the equation of motion oof both the blck and
the pendulum bob.
Fig3.
Q4: For the sprung pendulum shown in Fig.4, where the length ‘r’ is measured from
the equilibrium position of the massless spring, determine the equation of motion for
the mass ‘m’.
Fig. 4.
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Q5: For the compound Atwood machine shown in Fig 5,consisting of massless
pulleys and strings, determine the equations of motion of masses m 1 and m2
Fig. 5.
Q6: For the pendulum with an oscillating support as shown in Fig.6 with a massless
block and spring and no friction, determine the equation of motion on mass ‘m’.
Fig. 6.
Q7: For the block ‘m’ sliding on the moveable block ‘M’ as shown in Fig. 7 with no
friction, determine the equations of motion of both ‘M’ and ‘m’.
Fig. 7.
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Q8: For the cylinder radius ‘a’ rolling without slipping inside a larger cylinder of radius
‘b’ as shown in Fig. 8, determine the equation of the centre of the cylinder radius ‘a’.
Fig 8.
Q9: For a cylinder radius ‘a’ rolling without slipping on the outside of a cylinder as
shown in Fig.9, where the radius ‘r’ is measured to the centre of cylinder ‘a’,
determine the equation of motion of the centre of cylinder ‘a’ whilst it is in contact
with the larger cylinder.
Fig 9.
Q10: For the double pendulum shown in Fig 10, determine the equations of motion
on masses m1 and m2
Fig 10.
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