Question

Problem 3: The collar of mass m rest on a smooth rod, attached to two springs of unstretched length I. If the collar is displaced a distance s and released from rest, determine its velocity at the instance it returns to the initial position s=0.

Answer 1

given is

mass of collar = m

length of collar = d

spring 1 stiffness = k

spring 2 stiffness = k'

length of springs = l

now collar is moved s distance from position B to position A and then released.

applying conservation of energy principle at pt A and B

total Energy at A = total energy at B

spring1 potential energy + spring2 potential energy = kinetic energy of the collar

ks2/2 + k's2/2 = mv2/2

A S (4+4)

thus the velocity of the collar at the instance it returns to its initial position (i.e s = 0) is

Iktk S m