g-) Solve again the question by using the Lagrange’ s multiplier method. Two mas
ID: 1413139 • Letter: G
Question
g-) Solve again the question by using the Lagrange’ s multiplier method.
Two masses m and M are connected by a string of constant total length l = r + s. The string mass is negligibly small compared to m+M. The mass m can rotate with the string (with varying partial length r) on the plane. The string leads from m through a hole in the plane to M, were the mass M hangs from the tightly stretched string (with the also variable partial length s = l - r). Is this system holonomic? How many degree of freedom? What are the generalized coordinates? Write the Lagrangian of this system Are there any cyclic (or ignorable) coordinates? Write the Euler-Lagrange equations. Reduce the problem to a single second order differential equation and obtain the first integral of the equation. What is its pysical significance?Explanation / Answer
a) Yes , this system is holonomic .
b) It has 5 degrees of freedom .
c) Generalized coordinates are (l2 , 2r , s3)
d) Here, d(l2)/dt + d(2s)/dt = 2rs
e) No, there are no cyclic coordinates .
f) d2(l2)/dt2 + d2(2s)/dt2 = 2rs + d(rs)/dt
g) l = sqrt(r2 + 2rs)
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