A-spring-with-length-L-and-spring-constant-k-is-fixed-on-the-ceiling-Hang-a-mass-point-m-on-the-bottom-of-the-spring-Find-the-relation-between-distsnce-h-from-m-to-ceiling-and-time-t-Ignore-air-res

Question Number 182888 by CrispyXYZ last updated on 16/Dec/22

A spring with length L and spring constant k

is fixed on the ceiling . Hang a mass point m

on the bottom of the spring . Find the

relation between distsnce h from m to ceiling

and time t . Ignore air resistance, friction and

gravity of spring .

Answered by mr W last updated on 16/Dec/22

Commented by mr W last updated on 16/Dec/22

ω = \sqrt{\frac{k}{m}}

A = \frac{m g}{k}

x = A \sin (ω t - \frac{π}{2}) = - A \cos ω t

h = L + A + x = L + A - A \cos ω t

\Rightarrow h = L + \frac{m g}{k} [1 - \cos (\sqrt{\frac{k}{m}} t)]

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