I have three questions. I've worked on these for several hours and havn't come up with very much at all. Any help would be greatly appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

1.a perfectly flexible cable has length l. Initially, the cable is at rest, with a length xnaught of it hanging vertically over the edge of a table. Neglecting friction compute the length hanging over the edge after a time t. Assume that the sections of the cable remain straight during the motion.

(I am assuming the cable (l) is laying horizontaly on top of the table, then xnaught is hanging from the corner downward.)

For this problem the correct answer is x=xnaught*cosh(sqrt(g/l)*t).

How do you arrive at this answer?

2.A particle of mass m, initially at rest, moves on a horizontal line subject to a force F(t)=a*e^(-b*t). Find its position and velocity as a function of time.

Correct answers are:

v(t)=(a/(b*m))*(1-e^(-b*t))

x(t)=xnaught+ (a/(b*m))*[t-1/b(1-e^(-b*t))]

3. A massless spring of rest length l and spring constant k has a mass m attached to one end. The system is set on a table with the mass vertically above the spring.

a) What is the new equilibrium height of the mass above the table?

b) The spring is compressed a distance c below the new equilibrium point and released. Find the motion of the mass assuming the free end of the spring remains in contact with the table.

c) Find the critical compression for which the spring will break contact with the table.

(I don't have the answers to this problem. I just needed to check mine.)

Thanks,

Nick

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# Homework Help: Modern Classical Mechanics

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