Two wheels which are rotated by some external source with constant angular velocity in opposite directions as shown in figure. A uniform plank of mass M is placed on it symmetrically. The friction co-efficient between each wheel and the plank is μ . Find the frequency of oscillations, when plank is slightly displaced along its length and released.
Text Solution
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2 
Sol. If plank is displaced by x toward right then
Let N 1 , N 2 and f 1 , f 2 are Normal and friction force at Point A and B
by force balance
N 1 + N 2 = Mg ——(1)
and Torque balance
Mg ( λ + x) = N 2 × 2 λ ——(2)
by equation (1) and (2)
N 1 = 
– 
N 2 = 
+ 
So % f 1 = µ 
and f 2 = µ 
F.B.D of M
f 2 – f 1 = Ma
µ . 
= Ma = – 
.M
⇒ 
⇒ Time period = 2 
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