A very massive spring with a spring constant k and mass m' supports a block of mass m, as shown

Name: A very massive spring with a spring constant k and mass m' supports a block of mass m, as shown in the figure. Determine: a The Lagrangian of the system. b The equations of motion. c Show that the period of the vertical oscillations is T = 2π√((m + ((m')/(3)))/(k)). Assume that the velocity of the spring is proportional to the distance from the suspension point v' = (x')/(x)v and similarly for the mass dm = (m')/(x)dx
Uploaded: 2023-03-11T20:34:35-08:00
Duration: 2 min 13 s
Channel: Sri K

Question

A very massive spring with a spring constant $k$ and mass $m'$ supports a block of mass $m$, as shown in the figure. Determine: a The Lagrangian of the system. b The equations of motion. c Show that the period of the vertical oscillations is $T = 2\pi \sqrt{\frac{m + (\frac{m'}{3})}{k}}$. Assume that the velocity of the spring is proportional to the distance from the suspension point $v' = \frac{x'}{x}v$ and similarly for the mass $dm = \frac{m'}{x}dx$

          A very massive spring with a spring constant $k$ and mass $m'$ supports a block of mass $m$, as shown in the figure. Determine: a The Lagrangian of the system. b The equations of motion. c Show that the period of the vertical oscillations is $T = 2\pi \sqrt{\frac{m + (\frac{m'}{3})}{k}}$. Assume that the velocity of the spring is proportional to the distance from the suspension point $v' = \frac{x'}{x}v$ and similarly for the mass $dm = \frac{m'}{x}dx$

A very massive spring with a spring constant k and mass m' supports a block of mass m, as shown in the figure. Determine: a The Lagrangian of the system. b The equations of motion. c Show that the period of the vertical oscillations is T = 2π√((m + ((m')/(3)))/(k)). Assume that the velocity of the spring is proportional to the distance from the suspension point v' = (x')/(x)v and similarly for the mass dm = (m')/(x)dx

Added by Phillip T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

03/11/2023

Step 1

Step 1: The Lagrangian of the system is given by the difference between the kinetic energy and the potential energy. Show more…

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A very massive spring with a spring constant k and mass m' supports a block of mass m, as shown in the figure. Determine: a The Lagrangian of the system. b The equations of motion. c Show that the period of the vertical oscillations is T = 2π m' m+(3) k Assume that the velocity of the spring is proportional to the distance from the suspension point v' x' x v and similarly for the mass dm = m' -dx X