Question

A mass M is suspended at the end of a spring of length l and stiffness s. If the mass of the spring is m
and the velocity of an element dy of its length is proportional to its distance y from the fixed end of
the spring, show that the kinetic energy of this element is
1
2
m
l
dy
 y
l
v
 2
where v is the velocity of the suspended mass M. Hence, by integrating over the length of the spring,
show that its total kinetic energy is 1
6mv2 and, from the total energy of the oscillating system, show
that the frequency of oscillation is given by
!2 ¼
s
M þ m=3

Answer 1

sry cant understand it..use draw feature os something..

Answer 2

A mass M is suspended at the end of a spring of length l and stiffness s. If the mass of the spring is m and the velocity of an element dy of its length is proportional to its distance y from the fixed end of the spring, show that the kinetic energy of this element is

Answer 3

where v is the velocity of the suspended mass M. Hence, by integrating over the length of the spring, show that its total kinetic energy is 1/6(mv\[^{2}\]) and, from the total energy of the oscillating system, show that the frequency of oscillation is given by