abramsay
Sep1-10, 03:36 PM
1. The problem statement, all variables and given/known data
Help need with this problem.
A light spring AB of natural length 2a and of modulus of elasticity 2amn2 lies straight at its length and at rest on a smooth horizontal table. The end A is fixed to the table and a particle P of mass m is attached to the midpoint of the spring. The end B is then caused to move along the line AB so that after a time t the distance between A and B is a(2+sinnt). Denoting the distance of P from A by a+x, show that
d2x/dt2 + 4n2x = 2an2sinnt.
Find the value of t for which P first comes to rest.
3. The attempt at a solution
Here's my attempt so far, can't find the value of t for which P first comes to rest.
Am I right or wrong. Anyone has a better solution and a solution to the second part.
AB = 2(a+x) since AB at rest is twice a+x
At t, AB = 2a + asinnt
F = -k(x-e) where e is the extension and x the natural length
= k(e-x)
ma = 2amn2/a (2a + asinnt -2a - 2x)
a = 2n2 (asinnt - 2a)
= 2n2sinnt - 4n2x
a + 4n2x = 2n2asinnt
=> d2x/dt2 + 4n2x = 2n2asinnt
Help need with this problem.
A light spring AB of natural length 2a and of modulus of elasticity 2amn2 lies straight at its length and at rest on a smooth horizontal table. The end A is fixed to the table and a particle P of mass m is attached to the midpoint of the spring. The end B is then caused to move along the line AB so that after a time t the distance between A and B is a(2+sinnt). Denoting the distance of P from A by a+x, show that
d2x/dt2 + 4n2x = 2an2sinnt.
Find the value of t for which P first comes to rest.
3. The attempt at a solution
Here's my attempt so far, can't find the value of t for which P first comes to rest.
Am I right or wrong. Anyone has a better solution and a solution to the second part.
AB = 2(a+x) since AB at rest is twice a+x
At t, AB = 2a + asinnt
F = -k(x-e) where e is the extension and x the natural length
= k(e-x)
ma = 2amn2/a (2a + asinnt -2a - 2x)
a = 2n2 (asinnt - 2a)
= 2n2sinnt - 4n2x
a + 4n2x = 2n2asinnt
=> d2x/dt2 + 4n2x = 2n2asinnt